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It appears you are somewhat confused. Summer in Peru is December to March, so those months are the warmest throughout the country, that being the southern hemisphere. Peru is not very much south of the Equator though so summer and winter temperatures are not that different.
In terms of wetness, there summer is wetter indeed but that depends completely on the area. Coastal Peru is extremely dry and includes some of the driest desert on Earth. It is said that it never rains in Lima, although I did see a light drizzle once but really anywhere in the cost and slightly inland, you will rarely encounter any rain. There are plenty things along the coast where I used to lead Northern and Southern coastal tours, both have historic sights but those on the south are more famous and they have more tourist infrastructure.
The Andes is where things vary the most in terms of rain. It is cold there all year and it rains quite a lot from December to March. The cold and rain combination is particularly tough. Things are mountainous and get wet, so there is a high risk of mudslides. Many trails get closed temporarily for that reason. It is possible to visit pretty much throughout the year but as hitchhikers, as opposed to bussers, you will be much more vulnerable and since it is also cold and will be rather cloudy, things that get wet will take a long time to dry.
The oriente as they call the Amazonian basin east of the Andes is wet all year round. It can rain almost every day usually as strong bursts of downpours for a few hours and then clearing, rather than rain all day is it happens in other places. There are fewer roads there, so I would imagine this to be difficult for hitchhiking any way. While I have been to all of Peru, I am not very familiar with this region but while I was here, I relied on small boats mostly. Although I have been many times slight north in the jungles of Ecuador, which are very similar.
The high altitude plateau between Peru and Bolivia is cold but less wet year round. It still rains quite regularly with more wetness in the summer than other times but not as much as Cusco. There is quite a bit of traffic there and better roads than in the northern Andes. If you plan to go to this area make sure to get very warm layers of clothing and well protected tents.
You can check historical temperature and precipitation averages here if you would like. You will see, pretty much only the Andes and Oriente have much rain.
Upvote:3
After I've done the trip, I can share my experience. (Of course this is only anecdotic evidence: weather is not the same as climate!)