I lived in Ann Arbor for about a decade. I’ll do my best to answer some of these.
* On climate change, I think the Midwest is generally pretty good, and the models show Michigan as a green zone last I looked (especially moving a bit more north). But I don’t know that I’d make this a major buying decision.
* I’ve always felt the idea of lake effect snow was overblown I spent several years on the west side of the state, everyone warned me about the lake effect snow, and I honestly didn’t notice a major difference vs the Detroit metro area. You will get snow, but even now it doesn’t snow like it did when I was a kid.
* I’m not sure what options U of M has for auditing classes, but I’m guessing there is something. You’d also have Washtenaw Community College, and Eastern Michigan University over in Ypsilanti. I took some a Unix course years ago at WCC to fill the empty time in my schedule many years ago. It was pretty painless to sign up. Ann Arbor also has a lot of classes for seniors through the rec center. And of course private business… I took a knife skills course and some cooking classes at a local place there.
* The Ann Arbor library system is pretty decent and has several branches. UofM has several as well. I’m not sure what public access is like for UofM, as I never tried while I was living there, but I do remember going there in high school to find a rare book I needed. I tried to pop in to the Library at Harvard recently, when I was in the area, and it didn’t seem open to the public, which is the only reason I’m questioning of UofM would give you trouble.
* Ann Arbor is probably the most walkable city in the area, which makes sense due to the university. Also, the freeways on all sides bound it to prevent too much sprawl. Though you will want to be adjacent to the downtown area for prime walkability. They have also been putting in some protected bike lanes if you’re into that. Some of this, and more big apartment complexes downtown have left the city feeling more congested, it doesn’t feel quite as quant as it once did, but still has some of its charm.
* For cost of living… for Michigan it’s high, but if you’re coming from a coast, it probably won’t feel too bad. It’s really housing that is the main expense.
On the topic of snow… a lot of people from Michigan become snow birds as they get older. They spend most of the year in Michigan, then head down to Florida for a couple months in the winter. My dad has been doing this for the last 5 years or so (using something like VRBO). He also recently started hiring out to take care of snow removal. Or, if you choose a condo over a house, it may not be an issue at all. Just keep parking in mind, and getting to and from the car, if you’re looking for something like that near downtown. If you haven’t lived around snow before, a good hack is to walk on the grass to avoid an icy sidewalk.
The temps hovering around freezing, like they are now are the worst for ice. If it would get cold and stay cold, it seems much safer. But downtown Ann Arbor usually does a pretty good job keeping things clean.