Only if you're riding a papier mache frame with a popsicle-stick wheelset.

All kidding aside, I don't think felt would hold up to the elements very well. A couple good rains or some sleet kicked up on it and it would probably get absolutely disgusting. I would think more along the lines of something waterproof, one of the goretex equivalents or something. Maybe even canvas for something rugged-looking. Or naugahyde if you want to be really swanky.