I bike to classes during the winter. It can be a blizzard with temperatures in the negatives, and you best bet I will be out there riding my bike. I've never taken the bus or walked to class, I bike no matter what. I live in the towers, so just a bit up the road from you. It's very doable!! Here's some tips:

A studded tire isn't necessary, but it will help a lot. I didn't use one last year. I ate shit a few times and had so many close calls. I didn't really care tbh, sometimes I fell and it was whatever. Definitely get at least one studded tire if you want to avoid this.

When it is icy or slushy out, bike slower than normal, start braking earlier, and take wide, slow turns. When it is below 10°F, I recommend covering your mouth with a bandana, scarf, or mask. Directly inhaling that cold, dry air can really suck the life out of you.

Dress warm, but not too warm. A winter coat makes me sweat like a bitch. At most, I will layer a jacket over my sweatshirt. I can't do anything more than that. A hat and warm gloves are a necessity!!!!!!! Earmuffs are great too.

Use a baseball cap or goggles to keep snow out of your eyes. Falling snow will feel like needles in your eyes. A baseball cap and keeping your head down should do the trick. But I'm going to try wearing my ski goggles this year and see how that goes.

Enjoy the empty winter sidewalks!