As the PP said, you can nurse anywhere you want to. I just wanted to add that the mother rooms are centrally located so you are never that far from one (well...except maybe in Epcot).
If it were me, I would find an out of the way bench and use a cloth to cover me/my baby, but that is more because I would feel self-conscious. If you are comfortable without a cover then that is fine too. The far corners of some of the quick serve restaurants (Pecos Bill's, the ABC Commissary, etc.) would also be a good option if you want some privacy.