Nobody here can answer your question specifically. We don't know how you eat, what your basic response to muscle stress is, etc.
The best thing is to rest when you can (take the bus/ catch a ride with somebody, as mentioned above) so that the muscles have a chance to build faster. Otherwise, you'll still get there, it'll just be a little bit more exhausting for you.
Getting slicks for your bike will make a noticeable difference in both comfort and speed. If you are just biding your time until you can pay for your parking pass and aren't really planning to be a full time bike commuter, there's no reason to spend a bunch of money on stuff.
On the other hand, if you find you enjoy riding to work (as those of us in this forum do), then don't be afraid to upgrade your bike situation. You'll enjoy riding that much more (hoo-boy, then it really snowballs

).
Maybe I missed it in your post, but why will you be taking 9 months off of riding? I don't ride in the snow (though many people certainly do), so my down time is a few scattered weeks throughout Jan, Feb, and Mar. Don't let just the cold scare you.