Well I went to ASU in Tempe, and I can tell you that there is skiing in AZ. Mount lemmon is really close to Tucson. I believe its under a hour drive which isnt bad. Mount Lemmon isnt the best skiing, but its not bad, and its cheap. I haven't been there in a real long time. Az snowbowl is actually a decent mountain. Located in flagstaff az. A few hour drive from Tucson. Not too big not too small. They have a great bowl that you can hike up to hit some really nice lines. The elevation is crazy there, air gets very thin towards the top. The park isnt that good, but when the have snow its not a bad mountain by any means.
Then you have Sunrise park resort in the white mountains. This is the biggest ski area in all of Arizona, but it is also the flatest with a lot of cat tracks, and very low grades. They do have a decent park, and a pipe, so its kind of a trade off. Bottom line there is skiing in Az, and it is very very bad ass to be able to go skiing during the day and come back to palm trees, and pools after you finish skiing.
As far as u of a goes....its a good school. I would say Tucson is very much wild west redneck town, which is what detoured me from going there. Not sure what your major is...but the main reason I picked ASU over U of A, is because I didn't want to be in the middle of desert no where. I mean there literally is nothing around the out skirts of the town. I liked the city of phoenix better, gives you that city feeling, while allowing you to still enjoy all the outdoors have to offer.