Winter cycling is actually very nice if it's dry (I'm in Saskatoon; too cold for salt, and a winter melt is very rare). However, winter will be hard on your bike, especially if your area uses salt and sand and you get occasional melts.You also probably won't feel like bringing your messy bike in to clean and service it, and you REALLY won't want to work on it outdoors, which makes the wear and tear worse. I sure wouldn't be buying a new bike for winter... if anything, I'd be leaning more towards using a disposable beater.
Your Trek sounds like a perfect winter bike to me if you get studded tires, and don't mind abusing it a bit. I wouldn't worry too much about rusting out your frame; you'll ruin just about everything else on the bike before that happens if wet/salt is a concern. If you do get a new bike, just save it for nicer weather!
The only other thing I'd recommend would be to replace the grease in your bearings with something that will stay mobile if you're expecting to see temps approaching -20F (or colder). It will make the handling much safer; I had my bike out a few times at -40F last year, and that's about where my grease got so sluggish that it became impossible to move the handle bars; it seems okay at temps that are a little warmer, and then, boom... a couple degrees colder and you have no steering. I'll definitely be replacing the grease before winter hits this year.