Hmm. I hate to say this, but maybe look into getting a second-hand, cheap, or preferably free treadmill or elliptical machine? Just to walk and do mild stuff in, not to huff and puff mindlessly. I wouldn't suggest a stationary bike because I think those are way too low impact, being on your feet is what matters here.
Other than that, bundle up and brave the weather I suppose. It may derive a sense of accomplishment along with the exercise, you know?