My wife and I last went in September 2004, when hurricane Jeanne hit, and it definitely shut down the parks for that. We got there the day before the hurricane was scheduled to hit and the parks closed at 7pm that evening, and everything was shut down the following day, including all the restaurants. We were staying a the Boardwalk and they wanted everyone to stay in their rooms as much as possible, but they didn't really enforce that. They didn't let you go outside though.
Buffet style meals were available for a price (I forget how much), and that was essentially your only food option other than what you could find in the convenience store in the hotel. They did put Disney movies on all the Disney Channels, and the characters showed up at the hotels during the day everything was shut down. The hotel bars were open, so you could at least still drink if you wanted, and the hotel staff put out some balloons and coloring stuff for kids to play with.
All in all it wasn't great, but it was a good story to tell, and the weather after that for the rest of the week was perfect, almost too perfect, as we could have used a few clouds to tone down the sun a little.