I've commuted in Chicago winters for several years.

All the tips re: clothes, fenders etc are right on. Balaclavas are awesome below 25.

My best investment has been a good ($200-300) goretex shell coat (no insulation) with pit zips. I ride that in anything from spring rain (with a tshirt and the zips wide open) to five below (with several layers and the coat zipped tight). The pit zips are key for warmer (40+ weather). Very versatile and keep you dry and out of the wind. Get non-bike-specific (e.g. patagonia, north face) so you can use it everywhere.

I will vote against studded tires. In a winter, there are a small handful of rides that must be accomplished on snowy roads - usually when it is actively snowing at the time and the plows haven't arrived yet. Even aggressive tread is overkill. I'd suggest a light tread, with a small pattern rather than large knobs. Most foul weather rides will be on wet, salty roads.

Also, expect to go through some components. My winter commuter (an old Giant hardtail mounain bike, similar to your Trek) goes through a cassette and chain every season, due to all the salt and grit. I just buy the basic bottom of the line ones each spring for $30 and call them semidisposable. Brake pads and levers also take a beating. I go through a rear derailleur every few years, again just get a basic one; I've removed the front deraileur and just use the top chainring - no hills around here.