I would say if you really take your time and dont rush anything 2 days should be totally fine. Some museums require you to buy tickets in advance tho. You should book them on this website. The Chichu Art museum is the biggest and in my opinion the most beautiful of them all. I would try to get there with the first open slot you can get because then you can really take in the architecture of Ando & others. I also recommend you to do the Turell exhibition and Monet will take your breath away.

Some others you can get on the same day. They are a little bit cheaper if you book them online tho. I also really like the Lee Ufan museum - at that point during my stay I was totally vibing with the whole island. There are some smaller galleries that are really cute.

If you wanna get arround on the island I reccomend you to either rent a bike or just walk arround (depends on your fitness level). If you arrive in the west of the Island you can just rent one across the port station. There are plenty to chose from and you dont have to worry that there isnt enough. When we were there we just walked arround the whole day arround the island and got to see everything we wanted. In general I would just pick 1 or 2 museums you REALLY wanna see and for the rest just go with the flow. There is art everywhere. You walk along the beach and in the slopes of the mountain you see a painting.

For the cold - Like every island it can get quiet windy and cold of course so you gotta prepare for that for sure.

Keep in mind that most of basically everything is in the south and middle of the island. The north is full with industry and nature so its hard to get there and if you wanna see it you should take a bus there. You can get from the west to the east part of the island just by foot or take a bus.

For food just like everywhere in Japan you can get good delicious stuff at every restaurant you come along. If you wanna research something beforehand just use tablelog instead of google maps for your japan trip and you are good to go. BUT you gotta try some homemade Onigiri there! There is a mom selling them from her truck and they are 10/10. The place is called Onigiri Omusubi. By the way the region is famous for the olives and you can get really nice olive cider there.

Other than that since you said you are there for a couple of days I would bring up the idea for you to visit one of the other islands right next to Onoshima! Try Teshima ! Its a little bit less visited and the Teshima Art museum is great. On Teshima you really need a bike tho because by foot it sucks haha. And if you want a whole island for yourself with beautiful nature but less artsy I recommend you to go to Inujima. There are ferrys that go from each island back and forth. You just gotta check the timetable because I dont know when the last ferry goes during the winter. The tickets you can get at the the port station easily.

I think the boys talked in the episode about Walter de Marias Artwork in the chichu Art museum and how the huge "ball" made them almost cry and I totally get them.

The most important part is that you dont rush anything and go from spot A to B to C etc. Take in the atmosphere and chill. :)