How's your public transit, your tool collection and your wrenching skills? To me, these play a factor in your decesion. I cheap used car can be the deal of the century if you know a bit and are comfortable under the hood. It can cost more than something more expensive would have in the long run if you have to get it towed to the mechanic every time something comes up.
Then again, if you are referring to payments, you may not be thinking of the same definition of "cheap used car" I do. If you're thinking preowned with warranty, disregard. If you're thinking $500 special, the above applies.
Do you have anything like zipcar (zipcar.com) in your area? How far is your commute? Monthly payments could easily outweight the cost of a zipcar for the winter, or even public trans & cabs for a couple months. Also, if you're using public trans and cabs you'll be more likely to ride on the borderline days than if you have a car you're making payments on anyway sitting in the driveway. I would be anyway.