In Colorado we have much, much worse. CDOT uses mag chloride to melt snow, which can actually rust out the entire underside of a car in about 4 years if you drive through it enough. That stuff is freaking scary, and car warranties generally don't cover the damage because it just shouldn't get rusted that fast.
But for OP, Honda CR-V or similar is just about perfect if you're planning on being a broke college student/skier. Decent mpg, reliable, does well in snow, fits 5 people and skis and such.