Ok, so, even though I’m from Syracuse, NY (apparently the 4th-snowiest city in the lower 48) I think I can suspend my disbelief enough to help you out.
The real key to staying warm is layering. Lots of layers = more body heat that gets trapped inside your clothing. You probably want to stock up on plenty of sweaters (cotton »»> wool), maybe a couple good pairs of fuzzy socks, water-resistant footwear, a good water resistant jacket, and maaaaaaybe a pair of long johns. The most important thing I want to stress is that it’s not as if you’re buying all this as part of a winter outfit, but rather that they’re all components of what will become your daily wardrobe during cold, snowy stretches. You’ll be super warm with this setup regardless of what brands you choose to buy, so it’s pretty easy to go cheap as well.
I should also note that the buildings and houses on campus are really well-heated, so it’s not as if you’ll be bundled up all the time; this advice is just for days when you’ll be out of your house for extended periods of time.
The best thing about layering is that it’s easy to take off a jacket or a sweater to adapt to being indoors/outdoors. Some days you’ll only want a sweater and other days you’ll don the full suit of armor. Adaptability is key to survival, after all.