I'm planning for riding through the winter, but I'm not even sure which bike I want to use. I bought a Sears 3-speed to use, but I'm wondering if my Trek 8000 SLR would be a better choice or not.
3-speed Pros:
No Derailer
Already has fenders
Already has a rear rack
While it would suck, it's not a big loss if it turns to rust
3-speed cons:
650 wheels, I have a 26" wheel I can throw on the front, but I'll probably need longer reach brakes.
Haven't looked yet but I don't know if I can even get a knobby tire for the rear. (I still need to figure out what size the wheel actually is.)

Trek 8000 SLR Pros:
Aluminium frame, so that won't rust
Should give me a bit better control, probably would be more fun to ride too.
I won't feel like I wasted $300 on a bike I never ride
Trek 8000 SLR cons:
Winter takes a toll on bikes, I'd like to keep this one in good shape.
Derailers
Have to buy fenders
Might have to buy a new rack to get one that fits

My town doesn't take very good care of the streets in the winter. While I managed to do without last year, I really want at least a studded front tire this year.

Any advice on which bike to choose would be appreciated.

Sears 3-speed ? to each his own :-) Winter riding isn't the same everywhere, nor do riders have the same skill levels. Personally, here in Anchorage, winter riding is more challenging , I ride as good a bike as I can afford.some times its MTB sometimes my LHT ( fatties fit fine :-) ). All bike components wear out, do your maintenance , then replace stuff that wears out.