Congrads and nice to hear of other winter commuters here in Utah. I am downtown SLC and commute up to the U. I would recommend a less than nice mtn or cyclocross/touring bike. It will get wet and will get very salty from the roads, sidewalks etc so I would not ride something u really have lots of money in. A good mtn bike with a rigid front shock is a nice start. Looking for a chromo frame will help give a better/smoother ride. As far as tires, I use some ones sold through Nashbar that have reflective sides on them (700's). They are cheap, around $12. For the real snowy weather I would recommend full on mud/mtn bike or cyclocross tires. I have tried studed tires in the past with limited success. If you want to try studs, get a cheap pair of knobbies, then use small stainless steal screws. U can then seal up the inside of the tires using duct-tape. These are heavy/not effecient but can/do work. As far as clothes, I layer. I have a waterproof shell (top/bottom) and they r on sale at REI right now (they even have reflective strips on the jacket). A thermal underwear or just a polar fleece under. There are some wind resistent fleece or something the like out there too, again check REI, Patagonia, or Kirkams. For wet conditions meat baggies over the socks keep the feet warm but u can get toasty/wet from the inside. A good set of gloves is IMPORTANT. I often get away on most days with cow/leather work gloves lined with insulation. Many normal gloves will break at the seams easy and winter cycling gloves are pricey. Make sure you have a good head light/tail light. U NEED TO BE SEEN BY DRIVERS AROUND HERE. I would also suggest just riding around in the snow/adverse conditions before trying a full on commute to give u an idea on how your bike feels. If you care stuff, u can keep it dry by putting your stuff inside a couple grocery plastic bags and then place them into your pack.
I hope this helps. It can be done riding through the winter. The slushy days are the worst and most dangerous. Ice/slick roads you try to keep a constant direction/speed and make no quick moves otherwise you loose it. Fenders are worth there weight in gold too. I have the luxery of using TRAX if the days get too bad and then ride shorter distances. U might have the option with buses and loaded racks they have.
Please feel free to ask for more questions.