We were there during Charlie, and it was a Category 2 when it hit Disney. Sustained winds at 110 mph.
We were staying in Fort Wilderness and Disney couldn't have been better at keeping us informed, then evacuating the campground the morning before it hit. We were given a room at Port Orleans, and stayed there for 3 nights as they cleaned up the campground and gave everyone in our party a 1 day park hopper for the inconvenience

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Pretty much everything closed down at 6 pm the night Charlie hit, including the restaurants. Disney gave everyone lots of warning and time to get food. Charlie hit us at 11:00pm and we never lost power. It had never occurred to me before then, but all the power, phone, etc is buried at Disney!
The parks all opened the next morning on time, with the exception of Animal Kingdom. They wanted to make sure the animals were all ok before opening up. AK did open, just an hour or 2 late.
Most remarkable thing I saw was a tree blown over in front of the Brown Derby in HS. I have a picture of my daughter in front of it. What makes it remarkable is that two days later we were in HS again to find the tree gone, the stump gone, sod over the hole and topiary's covering the mound. You would never have known the tree existed.
All in all, while it was obviously a bit disconcerting to be in a hurricane, it turned out to be one of the most memorable events of our lives. It also showed us once again why we love Disney so much. They took care of us like we were one of their own.