Sorry to bring it up so early.... :)

Thanks all for the advice. I'm keeping my eyes open for a good deal on Craigslist. I don't have a spare bike, so if I can find a cheap one, I'll grab it. After reading all of the responses, it seems like 700x35 tires may work out fine. I'm going to try and find a cheap bike that will take the 700x35 tires. That way, the studded tires could be placed on either my current bike or the old one, and some of the parts will be interchangeable too. It may be helpful to be able to salvage parts in the event of a crash, or if salt completely destroys my bike.

There was a Fuji Touring Series III for $80 yesterday on Craigslist in Buffalo. It came stock with 700x35 tires, so the studded tires would have fit. Of course I just checked back and it is gone. Dang it. :(

Luckily I have a long time to shop before I have to worry about snow and ice.

Like some of the other posters have said, I'd worry less about the frame due to salt and worry more about what's going to happen to the gears, chain, and other components. The cost of replacing those things come spring might be more than just getting a decent beater bike. I'm personally of the mindset to get a beater bike for winter because even with studded tires, you can still slip on a patch of ice and ding your bike up pretty good.