When the road is blocked by animals, what's the proper way to proceed?

In a more general sense, what to do will depend on many factors, including: where you are, the size and number of animals, the type of animal, the type of road, the vehicle you are driving, how fast you are going when you first see the animals, local laws, whether the animals are attended by someone (a farmer for example), and so on.

In general try to avoid hitting animals at speed. Anything larger than a dog can do a surprising amount of damage to your vehicle. People can and do die in animal collisions.
Smaller animals can still cause expensive repairs. For example, I once hit a pheasant (a bird about the size of a chicken) at ~120 km/h; it died instantly but it also broke my light.

Most animals will move if you approach slowly in your car.

With herds of farm animals attended by farmers, it is best to wait until the farmer has moved them out of the road. Honking and flashing lights will get you nothing except rude looks from the farmer.

Horses are skittish animals and the usual advice is to give them plenty of room, and drive past slowly and quietly.

With large wild animals, you might have to wait until they move out of the way in their own good time. I once had to wait for a rhinoceros to cross the road. I certainly wasn’t going to get too close, or get out of the car for a closer look! I just reached for the camera.

Obviously don’t get out of the vehicle if the nearby wildlife could be dangerous, and close the windows if one approaches the car. You probably wouldn’t want a lion climbing in through the window, while you are trying to photograph the zebra in the road!

At night, the problems multiply. Many animals seem to be confused by headlights, and will just stare at them approaching. Other might run towards the lights or further into the road. On a trip to Australia, I was told to drive slow because Kangaroos might try to hop over the approaching lights, only to be struck by the windscreen.

Local laws might also have something to say: in India don’t kill a cow; many places require that you report accidents involving livestock to the authorities.

To add to the other very good answers already posted:

Remember that for most animals, a road isn’t really their ideal place to be. There’s nothing growing there to graze on, and the ground is hard and hot. For that reason, most animals you’ll encounter are actually in transit over the roadway (just like you), not congregating long-term. Try to judge which way the animals are moving. If they’re moving across the roadway, your best choice is generally to wait it out. If they’re walking up the road towards you, put the vehicle in park and they’ll usually divert around you. It gets tricky if they’re moving in the same direction as you. You’ll be approaching from behind so they might not notice you at all. If you can’t get their attention, you might be stuck joining the herd and moving at their speed. Some animals naturally follow established trails (like domesticated cattle or horses). If they’re walking down the roadway the same direction as you, you may be able to pass them by driving slowly on the far shoulder.

Cars are confusing to a lot of animals. It’s a big, square-ish boxy thing that doesn’t look like anything out of the natural world. A lot of animals don’t know how to react to one, but will react fairly rationally if you can communicate that you’re actually a human. Waving out the window or sticking your head out the sunroof can get the message across. A buddy of mine used to work on the highway patrol in a rural, mountainous area and would get elk and caribou herds off the road by rolling down the windows and turning on the radio (he claimed it worked best with music that had more vocals and less instrumentals).

Of course, some animals are special cases:

• Birds are the trivial case. Approach them slowly and your size and noise will scatter them. If they’re carrion feeders, beware of roadkill.
• If you encounter bison in the road, stop your vehicle at least 20m away from them and wait them out. You’re not going to convince them to move, you’ll just irritate them. Bison will headbutt your car if they get irritated, if they feel threatened, or just because it’s Thursday. They’re serial headbutters, completely irrational, and can do massive amounts of damage. Bison are also natural trail-followers and have a habit of walking down the center line of a highway. If they encounter a parked, stationary car, they’ll take a step to the side, walk past the car, then step back to the center line and continue their journey (as if you were just a funny looking rock).
• Most cattle will also just walk around you if you’re stationary. Pay close attention to the horns, though. Some breeds have extremely long horns and have no qualms scraping your car as they walk past. Pulling onto the shoulder and out of their path as far as possible will help minimize damage.
• Try to get out of the path of goats, even if it means pulling off the paved road. Goats are just as likely to travel over your car as they are around it, and those hooves can do a decent bit of damage.
• Be particularly careful with pigs. Even if you think they’ve left, there can be one right in front of your car. If you hit a pig, they can roll up under your car and do a lot of damage from the bottom. Try to count them as you approach and make sure you see the same number leave.

Specific to deer (and perhaps other ungulates) in the night-time: the phenomena of deer frozen in the headlights is well-known. I encountered it once. Flashing high beam (from dipped beam) did nothing. Switching to sidelights did: the deer relaxed and moved away as soon as I switched.

The deer weren’t entirely frozen in my headlights. My car was one of those where the front dips noticeably when braking. The deer reacted to this as if I was trying to herd them along the road. (I think it’s because male ungulates lower their heads to direct their herds. I wouldn’t be surprised to see horses react the same way.) The solution was to avoid sharp braking, especially because the gaps for the animals to leave easily were right there. (I’d be very wary of trying to use this trick to move animals, anyway.)

Most “kinda tame” animals such as the ones in the photo (horses) will move away if something big approaches. As will many, but not all “wild” animals. Most will, without panic, avoid something that makes (moderate) noise, most will react rather negatively to something that makes sudden, harsh noises or is moving rapidly. Most animals will react favorably to being gently pushed with your palm by moving away. Believe it or not, the palm thing even works on curious sharks (who are just wondering whether you’re edible or not).
Yes, an aminal (horse, cow, ox) that is easily 4-5 times as heavy and easily 5 times as strong as you are will (usually) just move away if you push it gently. No, they will normally not attack you (or bite, or eat you, whatever) unless you behave like a jerk. The overwhelming majority of animals is surprisingly indulgent, friendly, and obedient. Unless, well… unless.

There are of course some very obvious and some not-so-obvious things things to pay attention to. For example, it is an utterly stupid idea to get rough on or frighten an animal that is 5 times your weight. Chances are 50/50 that it will go away anyway, but it may as well kick you in your belly or let you feel its horns which you probably won’t recover from.
Another obvious, and utterly stupid thing is to get in between cow and calf, or in between cow and calf, and stallion. Do not ever do that if you value your life. An angry cow that defends its calf will tear your car to pieces, with you inside. And oh heck, they don’t look like it, but they do run faster than you can run.

Honking from a distance, may very well work with many animals, and will be safe, but it may be needlessly stressful for the animal (you might care or not!) and it may not work with some.
For example, mules are well-known to be “stubborn” and if they don’t like, they do not move even when you beat them. Well, truth is, they cannot (and certainly will not) move because they’re in shock paralysis. That’s their innate behavior. So, in that case, honking or shouting may not be such an ingenious idea because after that they’ll never move. Deer is known to be attracted by light, and other animals might freeze in place when exposed to the blinking. So while flashing lights may work, it may as well not, I wouldn’t rely on it.

Then of course there’s animals that you simply don’t want to approach (crocodiles, lions, dingos, apes) for a variety of reasons. So the thing about getting out and pushing them away with your palm doesn’t apply there. Wait until they move by themselves (best idea!), or slowly drive on (pedestrian speed), and rely that they move away, if you really must.

In the UK, the Highway code offers specific guidance:

Rule 214
Animals. When passing animals, drive slowly. Give them plenty of room and be ready to stop. Do not scare animals by sounding your horn, revving your engine or accelerating rapidly once you have passed them. Look out for animals being led, driven or ridden on the road and take extra care. Keep your speed down at bends and on narrow country roads. If a road is blocked by a herd of animals, stop and switch off your engine until they have left the road. Watch out for animals on unfenced roads.

Note that as per the final comment, herds of animals will not necessarily be attended, so you may be waiting a while for them to move on… Also, even if there is fencing, sheep seem to be experts at finding their way through, so remain a potential hazard.

It depends on the species.

If you’re driving in Sápmi (Lapland) and there are reindeer on the road, shout at them. They’ll understand a human voice much better than a car honk or engine. You may need to get out of your car so they can see as well as hear you. If you just honk, they will probably just keep staring at your car in mild curiosity. If you do nothing, chances are they do nothing either (and you as a tourist might be OK waiting 10 minutes admiring reindeer, the local behind you, who has seen reindeer 300 times already and is trying to get somewhere, may be not so happy with an unneccesary wait).

Reindeer are not dangerous to humans (except indirectly by triggering traffic accidents when people think it’s “safe” to drive 140 km/h on the “empty” roads in the far north), but they might damage a car: a friend was sitting in their car waiting for reindeer to leave, when instead the reindeer walked close to the car and broke off the outer mirror, oops.

(Noisy!) reindeer on a side road near Kilpisjärvi, Finland, 2009-07-01. Typically, they appear to prefer grazing on the road to grazing next to the road, and in this case are teaching the calves to prefer the same.

Source: personal experience when I lived there + talking to locals. I was first told this by my Swedish teacher in Luleå, Sweden, in 2005, but heard the same advice from others several times later.

First, look for people. If the animals are with some people, just sit tight and wait. A few minutes won’t hurt you. The people can see you, you don’t need to make noises or otherwise let them know you planned to drive through here. They know that.

Second, evaluate whether you think these are completely wild animals (monkey, moose, elephant, rhino) or likely to live on a nearby farm (horse, cow, llama, camel). Wild animals are more likely to attack you and less likely to respond to any kind of “get out of the way” signal from you. This is partly because some species have behaviours that don’t suit being farmed (in other words there’s a reason you don’t see fields of tigers), and partly because on a farm, individuals who don’t respond to signals and orders tend to go to slaughter or otherwise leave the farm.

For animals you think might be at least somewhat habituated to humans, slowly driving forward and seeing if they move aside, flashing lights, patting the side of your car, and other mild things are likely to work. If they don’t, stronger things like sounding the horn probably won’t — I would save them for a last resort. If there are no animals behind you, backing up carefully to wait for a gap you can go through is also a viable strategy. For example, in the picture in the question, there is a wall on one side but the other side has a wide grass area you could probably drive on for a short distance. If you have no shoulder or grass to drive on and animals are all around you, so you can’t back up, then sounding the horn might be helpful to either move the animals or attract their farmer to help you out.

For animals you think are wild, keep your windows up, don’t move suddenly, and don’t sound your horn. Animals rarely stand still out in the open for long periods of time, and especially not when they have company. Depending on their size and how many there are, patience may be all that is required. Or, as with the farmed animal, backing away and perhaps turning around to go back and find another way through, or a place to wait for a while. If you’re trapped, then louder noises may be one of the only options you have, even though it might cause them to startle and run into you or another car. It’s dangerous, so don’t do it lightly. Same with driving towards them if you have no reason to know they understand what a car is. You might end up doing it but not without a good long think.

The picture is of horses in the road. When I stayed with friends in The New Forest, UK, where free range ponies roam (not actually wild), they often block the road in groups, and nothing apparently will move them. But my friend taught me how:

• Be gentle, do not alarm them, give them time.

• Open the car windows, so the ponies can see you, and then

• Lightly pat the door panel with the palm of your hand continually.

This worked a treat, the ponies gradually move out of the way.

In my country, since it’s a large country with a lot of long highways across deserts and mountains where a wide range of animals cross the streets (mainly camels, baboons and donkeys), I have faced that a lot.

I am unaware if there are laws for this, but out of personal experience I learned a few Dos and Don’ts:

• Before approaching them, ensure no cars on the opposite road, cars can be going fast and you might scare the animals away to the other road and cause a nasty accident.
• TURN the warning lights on to alert other drivers behind you. This sometimes scares the animals away and you’re done.
• DO NOT stop in the middle of the road.
• DO NOT get out of the car, animals regardless of how cute they look, they sometimes decide to attack.
• DO NOT drive too close to them. You might get your car dented or the animal injured.
• DO NOT feed them, this is a common mistake people do. In fact, animals will memorize this and then come back for more. Check the photo below.
• WAIT a little bit, take a few photos, they usually move on their own. This is your best and safest bet.
• Use the headlights, on and off rapidly, it might scare them away.
• If they do not move, as I said before, ensure no cars on the opposite road then honk gently.
• If that didn’t work, try to go around them, as far as possible from them.
• Finally, call the local authorities, we do that to ensure they fix the fence. The highways in my country have fences (usually for larger animals like camels).

The following photo (taken from the internet) is for a highway in my country, on the highway to my home town, baboons are regular visitors now and they can cause serious delays and accidents sometimes just because some feed them:

I would wait at least a few minutes. There does not seem to be anything edible on the road, and there are some tasty (to horses) looking weeds on either side, so they will probably not stay on the road for long.

If they do not move in the next 10 minutes or so I would slowly edge the car forward. Honking, or any sudden move, might spook them, creating risk of injury to the horses and damage to your vehicle. They may be desensitized to car horns, but you do not know that.

I would get out of the vehicle to discuss the matter directly with the horses if, and only if, I knew and trusted them. If you know a given horse well enough for you to be safe approaching it on foot, you know what cues will get it to move off the road.

Stay in your car, as in the car you are a car and not a danger or enemy. Walking you may be seen as danger and the animals may try to scare you off, which can be dangerous for your health.

If you do have the time, I would wait and enjoy. But if it takes long or if you are in a hurry you can drive slowly forward. Most of the animals living near roads are owned by people and get handled at times. And as such they are used to be driven and a car coming up to them will feel like that.
But do keep your distance, at least a yard/meter, I’d say. If they do not move when you are that close, just wait a bit longer.
If you want to scare the animals of by sound, revving the engine is a milder sound than honking and it should work. You can follow it by a louder sound.

Disclaimer, I am not familiar with the local laws and customs in Chile, this is the general ‘wild and hardly handled big animals’ guide I read for several countries.