I'm usually on campus pretty late and have a 30 minute commute home on city streets well after dark to give some perspective. You just have to be smart. If you know it hasn't snowed, and roads are plowed and salted, you can ride pretty quick (as quick as studded tires will allow, anyway). Otherwise you slow down and take it easy. Studded tires won't let you magically ride on ice as though its normal pavement, but they make a world of difference in terms of traction.

Layering is a personal thing op. While I agree that wool is probably the best choice, I've gotten by on the cheap without it. I typically rock under armor under my clothes, and if its around 30 degrees F a hoodie is all I need--you are on a bike, and assuming you have a commute over a mile or two, will warm up. When it gets down to 20 wear the above with a winter coat and scarf. Below that I tack on a sweater et cet. A hat under your helmet is great, but you'll sweat an awful lot if its above 20, so consider a headband or those behind-the-head style earmuffs, and wear some gloves. I'm sure that bike specific gloves (lobster claw style et al) are awesome, but I've gotten by with cheap mittens. I know a lot of people swear by goggles, but I wear glasses and they fog up enough to impede vision under them, so its never my cup of tea unless its below zero. Experiment a bit, be more cautious because of the ice, and have a few dollars for the bus if you are under prepared and you'll be fine, and might find yourself enjoying it. Winter riding sounds tougher than it is, I usually actually really enjoy it.

Edit: If you really don't have clearance for 32c, you could consider finding a cheap winter frame if UT gets enough snow. I guess I'm maybe a little over-cautious, but as I ride in a lot of traffic, I would not want to do without my studded tires. I haven't had fenders because I definitely do not have the ideal bike for winter commuting, but if you layer right (and wear a waterproof back pack or mess bag if for no other reason than to absorb the water your rear wheel throws up) it really won't be that bad.