What were the capabilities of a warhorse?

Moving my other comment to a main answer:

Destriers would have been "short and muscular for power, but agile and good sprinters." 15-16 hands high and 1200-1400lbs describes baroque horses (especially Spanish/Iberian horses, who were extremely popular war-mounts), and stock-type/Foundation Quarter Horses (short but heavy, fast, and in modern times are often called "little tanks" or "brick walls"). This link to the National Foundation Quarter Horse Association has a great photo montage of famous Quarter Horse sires.

A scouting party or a messenger could easily cover 30-40 miles in a day, but according to A Collection of Unmitigated Pedantry, regular travel speed of most armies would be much slower, at 10-20 miles per day. Not because the horses can't go farther/faster, but because in medieval times, they have to keep pace with THE INFANTRY AND SUPPLY WAGONS. What use is covering the maximum distance if you and your horse are gasping for breath, and THEN you've left your food, your backup teams, logistics workers, and baggage behind?

Here's a shot of a modern-day working Quarter Horse from an AQHA News article; this horse and rider would look right at home with the Foundation Quarter Horse sires in the first link. Note that while Quarter Horses are certainly thick in the barrel and wide-chested, they are clearly very fit, and a chunky draft horse or a tall and greyhound-like Thoroughbred would have a MUCH harder time getting almost shoulder-to-shoulder with a calf.

Quarter Horses are famously built for a destrier's "sprinting" since they can reach speeds of 50-60 miles per hour (100-120kph for metric) over a quarter-mile's length, so most races take about 30 seconds. But this is exhausting, so a PRACTICAL sprint (where you need enough energy to avoid getting killed after your first five minutes) would "only" be around 30-40mph / 60-70kph.

Despite their heavy weights, working Quarter Horses should NOT look chubby like some modern draft horses, or "bodybuilder-defined" like modern halter-type Quarter horses (who are about the same weight, but often have notorious health issues like spindly legs and poor body structure). Muscle is a lot denser than fat, so a 1000-pound horse may well look "overweight" if they're out of shape, while a muscular one like the horse above may actually look "thin" to people who are only used to seeing pleasure-riding horses that go on trail rides twice a week.

Quarter Horses and the United States' ranching tradition are notably descended from "Spanish" horses and ranching, of which the most famous is the modern Andalusian. "Spanish" horses were extremely popular among medieval nobility for their bravery, their good looks, and agility, and also known for... bull-fighting.

WARNING, THERE IS INEVITABLE VIOLENCE IN THESE PHOTOS.

This photo is from Wikipedia's "Spanish-style bullfighting" page, a copy of Francisco Goya's artwork.

The second photo is from Wikipedia's "Lusitano" page. Technically, Lusitano horses are from Portugal, but they and Andalusians are well-known to be closely related.

Note the striking similarities between the bullfighting photos in Europe, and the Quarter Horse roping cows in America. The bullfighters have prettier clothes, but none of the pictured horses are exceptionally tall or draft-like; moreover, they're all sprinting TOWARDS or NEXT TO a charging bull/calf instead of AWAY, so personality and athletic training clearly trumps "immense size." Replace the angry cattle with angry humans, and you've got a skirmish.

Meanwhile, the website helpfully called "Destrier" has a detailed description of warhorses:

"Contrary to popular belief, the medieval knight was not mounted on a huge plodding draft horse like the famous Shire. By combining archaeological finds with pictorial evidence we can paint a picture of the typical Destrier as a very athletic short-backed horse not exceeding 15.2 hands in size.

Medieval paintings often show horses in perfect collection with beautiful gaits, permitting the conclusion that the medieval warhorse was highly trained and extremely manoeuvrable."

Here's a Facebook photo link to one of their albums. In general, "Destrier" shows a whole range of average-height horses that still have the personality AND body-type to get the job done. Some of them do seem like cob-types or smaller draft horses, but the largest modern-type drafts that are 18 hands and twice as wide as normal horses? Notably absent.

Why is that? For medieval safety-precautions, that's why! Most knights preferred short horses because it was easy to mount up, and contrary to pop-culture depictions of knights getting hoisted onto their tall and bulky draft horses, combatants prided themselves in vaulting straight into the saddle, sometimes without touching a stirrup. If they DID end up needing help (such as after getting wounded or exhausted), I imagine they just needed a step-stool, a log, or a boost up from someone else--not something that civilian horse-riders would find unusual.

Here's another Facebook link to a group shot. The note that destriers are usually 15 hands high (five feet tall) and "don't exceed 15.2 hands" would probably not be a hard-and-fast rule, since that extra 2 inches for 16 hands (54 inches) isn't a lot of difference. While five feet and a few extra inches SEEMS pretty short at a human teenager or small adult's height, remember that actual 15-hand horses are five feet tall AND five feet long, plus their necks and heads are famously mobile and often make them SEEM to tower another foot or two above a human's head; in the second shot I linked, most of the riders are adult men in full armor, but do NOT seem "too large" on their mounts.

Also notice how most of the destriers in that shot don't have armor? This is why they don't need to be excessively huge. Jousting armor was notoriously heavy, but it was ultimately for a sport where people did NOT want to get killed (too) easily, and they definitely wouldn't want their expensive HORSES killed if they could help it. A set of human combat armor is often considered to be half the weight of jousting armor, because combatants traded more mobility and speed for less protection/bulk.

Imagine how expensive a full set of horse armor is. And even if you can afford it, who's going to carry it, repair it, and clean it OUTSIDE OF BATTLE? Not your everyday man-at-arms or a noble's second or third son, who may be fine with his loyal horse and his set of weapons/armor, but often needs a job in a richer noble's garrison to MAINTAIN that horse and armor. That's usually how most castles filled their cavalry positions in the first place, as junior nobles and richer commoners were all over the place.

I imagine that real-life soldiers facing cavalry would NOT see a herd of 15- or 16-hand destriers and think, "that's the height of a thirteen-year-old girl, they're not THAT big!"

I can't find the reference at the moment, but it is a notorious problem in period-pieces that when a FAKE cavalry-charge is being filmed, the actors playing foot-soldiers constantly break formation. They know they're not in actual danger, and that the riders won't actually smash into them, but they still can't fight their self-preservation instincts to run away from a wave of galloping horses. Which, if I remember right, is basically the point of cavalry as shock-troops / morale-breakers.

The last photo link is here, and it's a shot of a foot-soldier "fighting" several cavalry members in one of Destrier's reenactment battles. Notice how all these "average/short" horses still basically dwarf him and his shield, and he wouldn't have much more advantage if he stood up? In real life, this guy would be "brave for his last thirty seconds." There's a REASON infantry holding the line against cavalry is rare, after all.

I can answer only partially.

The most powerful horse breed I regard to be the Ardennes horse. This breed was able to carry a fully outfitted knight into battle.

The fastest war horse would be light cavalry as used in the Napoleonic and Krim wars. A charge's maximum speed was 20 km/h. It could be kept up only for a short period of time.

Cavalry travel speeds would have been much lower especially in unsafe conditions. Here probably steppe nomads like the Huns or Mongol armies would have been fastest.

For messenger speed a good candidate is the Pony Express with 1900 miles in about 10 days.

References:
https://en.wikipedia.org/wiki/Ardennes_horse
https://en.wikipedia.org/wiki/Horses_in_warfare
https://en.wikipedia.org/wiki/Pony_Express

Ann Hyland wrote two books on The Warhorse with different subtitles re the time periods covered: the first ancient and medieval, the second Renaissance and modern. She also wrote Equus on horses and mules in the Roman realms.

First, wash out any images of knights on Shires and other big draft horses. Draft horses are for draft, are weak in the back for carrying, have gallumphing gaits, and only developed in the later 1700s, but mostly in the 1800s. Shires get their height from Thoroughbred blood. (Silver, Horses of the World)

Thoroughbreds were developed from the 1600s forward as cavalry remounts (Osmer, On Horses), and one of the qualities desired was speed. So they developed as racehorses. They are the fastest breed.

Now, you can erase all this modern stuff because medievals didn't know about it. While Svinhufnud did translate an Anglo-Saxon horse care text, we can see from that the medievals were still largely basing choices in riding horses on Xenophon, On Cavalry, c.350 BC. (You can get a translation at Project Gutenberg or the Perseus Project.) What makes a good horse for the job had not changed.

A good-sized warhorse was 15hh, and a hand is 4", measured to the withers, the pointy bit behind the neck. Hyland bases a lot of her sizing on horseshoe sizes, and surviving saddletrees. Smaller was common. The look of the horse was like a heavy hunter. Roman noses were the norm. Look at statuary. The Frisians of today preserve much of the look, and so were used in the movie Ladyhawke. A Frisian/Saddlebred cross is possibly closer, and a completely droolworthy beast.

Warhorses were called destriers/dextriarii because they went on a dexter lead (our left lead), according to S. A. Bolich. This put the support in the right place for crashing your lance into someone else. On the right lead, the horse is far more likely to fall back. So they took special training.

It's controversial whether they had haute ecole training (like the Lippizzaners in Vienna), if this would be any use in battle, but a horse fighting footsoldiers under saddle is reported as far back as the Graeco-Persian Wars. The Athenians had a special bounty out on Mardonios's warhorse because it was such a terror. You can also see haute ecole poses in the Elgin Marbles. Bolich says it could work, and it would seem to be required to take on a phalanx.

As to travel: depends on breed, condition, supplies, and roads. Not to mention climate, weather, and necessity. Some Mongol horses probably travelled from Mongolia to Europe. I would need my notes at home to quote weights of armour for the destrier.

Talked with my favorite professional historian (who is also a professional equestrienne).

She pointed to the Tevis Cup as one source that might be instructive. Most of the Tevis competitors are Arabians, who have been bred to run fast and hard on minimal water & care. They shed heat well, but they can't carry the weight of someone in armor. (There is a reason you'll find few suits of Bedouin plate mail.) Depending on your interest, you may also want to search for the Mongol Derby (friend of a friend rode that last year) as an example of endurance riding.

They don't "march" - and their travel distance isn't limited by political conflict, as much as it is by fodder and terrain.

It is an error to assume that larger horses can carry more; larger horses are generally built for pulling. The Royal Armouries use a 15.2 (60") hands Lithuanian heavy draught as their model for displaying 15 &16th century heavy horse armor because it fits well (although see below; recent research may update that model.); that may be useful as a visual model. Note that the picture of the Ardennes horse does not even remotely look like a contemporary Ardennes horse. The breed shifted dramatically in the 19th century.

She concurs with the Wikipedia article that during the middle ages they conceived of "breeds" rather differently, and tended to categorize the horse by use rather than by genetics. That article may answer many of your questions.

Aside: you commented that as an urban dweller, you've never seen a horse, but you've doubtless seen a dog. "horse" is as broad a term as "dog" - dog's include terriers bred for ratting and massive dogs for pulling, dogs bred for speed (greyhound) and dogs built for raw aggression.

She also strongly objected to comparing a knight's horse with a messengers'; that is a little like comparing the Chevy 2500 she uses to haul her horse trailer with my ex-wife's old Fiat. (or to use the analogy above, like comparing husky with a greyhound). Sure they both have 4 wheels, but if you hook the fiat up to the trailer, all you're going to get is laughter. The knight may charge into battle atop a destrier that is some form of draft horse, but he will ride a smaller horse to battle (a rouncey), and include a few pack horses in the train. The fuel consumption for the draft horse is going to be rather different than that for the rouncey. And the messenger is going to ride something that emphasizes speed and endurance. (there is a reason that modern jockeys must maintain a weight under (IIRC) 140 pounds; those horses are built for speed).

The typical formula for the capacity of a riding horse is 20-30% of the horses weight, assuming the horse has been bred for riding, not pulling. (This is a general principle; horse people will argue with me on this.) Riding horses are built to tolerate a load on their back; pulling horses are bred to apply force through a horse collar or yoke. They have different anatomical structures. Draft horses can pull up to 58,000 pounds, although that isn't really relevant to the medieval knight - that is pulling, which is not a combat activity, and it is a modern horse that is larger and more powerful than the historic horse.

She also objected, as I did, to comparing horses across the range of human history excluding only the past 100 years. She said that comparing horses across all geography is probably even more absurd. Native Americans riding horses across what came to be Kansas have different challenges than trying to cross the alps, or ride into Russia in winter.

There is another reason why your question is difficult to answer; take for example your question about their top speed while charging. They lie. They didn't have speedometers, and contemporary estimates of speed are going to be in units that emphasize poetry over accuracy. There is no real reason to record a horses charging speed; if you're in front of the horse, it is too fast. It isn't running as fast as a race horse.

Generally H:SE prefers that you consult Wikipedia and other common sources before you ask questions here, but I thought perhaps her comments and some sources might be useful to you. If you are interested, I can reach out to another contact who is a professional jouster.

A few sources:

• The wikipedia article - she consulted that while I was writing this and said it is fairly good for the issues you want.
• Horses in Shakespeare's time (Anthony Dent) - An ordinary traveler will rarely make more than 30 miles/day (and that is on roads, switching horses to avoid tiring the horse). I think that 30 miles/day is therefore an upper limit of operational range, depending on terrain, etc. Not a lot of warhorse in this book, but good reference material for some of your underlying questions.
• Xenophon - if you want to know about the military use of the horse rather than about European Chivalry.
• Your local SCA chapter or ren faire; they are generally happy to talk about their horses. (Have a friend call you after a half an hour, or prepare another escape plan).

Update - recent research indicates that warhorses were much smaller than we had previously assumed - perhaps 14-15 hands average. (under 5 feet high at the shoulder). Both my favorite professional equestrienne and I ride horses who are larger than that (16.2 hands (64 inches) and 18 hands (6') respectively). The general definition of a pony is 14.2 hands, so some of the destriers would be classified as ponies today.

Final note - although you didn't ask about it, one of the predominant capabilities of a warhorse is calm. This is difficult to explain; I've been riding for a couple of years now and I still have trouble grasping it. Horses are prey animals - they are genetically determined to flee danger and to assume that any unexpected stimulus is dangerous. Although the horse I ride is quite calm and stable, I can't use her for mounted archery because she flinches at the sound of the bowstring. Far more important than size/speed/endurance or any other factor is the training to allow a horse to endure combat - to race towards loud noises and unpredictable stimuli. Some of that is training, but some of it is psychology. Some horses have it, some don't.