If severe weather is imminent, I would take shelter wherever you are to be on the safe side. If it's just rain, I agree that you should put on a poncho, pull out your umbrella if you have one, and stay in the park. Take a deep breath, accept the fact that you are going to get wet (probably even with a poncho and umbrella), and keep to your touring plan to the extent that the weather and attraction closures allow. If you don't have waterproof sandals, have an extra pair of dry, comfortable shoes in your room as a backup until your wet shoes dry. As far as severe weather, I have been in Epcot during a bad thunderstorm, but I don't remember any restrictions. I was in the Christmas store in Downtown Disney during a tornado warning, though, and the cast members wouldn't allow anyone to leave the store until the warning expired.