I dunno, depends on how rusted things really are. The outside can be fairly beat without compromising the frame. That's not a promise, but you can figure it out fairly easily by pulling off the cranks, stem, and seatpost. If the frame isn't compromised, you might consider whether the parts are serviceable for your needs on a winter beater. Maybe a little grease and a new wheelset (or even converting a used but functional wheelset) will do the trick. There's plenty of info online for doing this stuff (sheldonbrown.com). If you do go that route, just know it'll cost you a good bit of time.

If the frame is toast or you're not into wrenching, you can still pick up a cheap, functional bike and convert to SS for far less than the price of a new frame. Even if it's just for the frame and you want new components, old frames are great, far cheaper, and potentially higher build quality than a new $100-200 track frame.