Disney closed all theme parks at about 11:00a.m. on 9/11.
Most guests spent the day at the pool, and there was a message left on the Voice Mail in our room later that day stating that Disney theme parks would operate at normal hours on 9/12, but I have to say most people left as soon as they possibly could and although flights weren't going out it was amazing how many people had relatives drive in to pick them up or rented cars or even U-Hauls to drive home.
Disney will only close for as long as they feel it is absolutely necessary. While I truly believe they would never put any of their guests in harms way, they have to be prudent because they lost a ton of money on 9/11 and have been losing more because of it.
By the way, they did hand each of us one day park passes as we evacuated the park.