We missed them, at Disney 9/11-9/18 and had HOT but wonderful weather -- much nicer than any of our previous trips to Disney. BUT, maybe 5-6 years ago, we WERE at Disney when I "think" it was Floyd came very close to the parks. At that time we stayed at CB, which to be honest, I wasn't that crazy about. To be fair, it was the first time Disney had to close a park, and it was a little weird (to say the least) but ok, we felt safe (altho I was VERY nervous).
I think they are more seasoned with these types of emergencys and shut-downs now, given the weather and world events of the past few years.
We stay at the YC, consg. floor now. And were told that when the first storm came through, they tried to make it almost a party atmosphere, with music, and a buffet set up for guests. And a guest commented that they felt as tho they were on the Titannic, given the atmosphere of the resort

When the second one came, they were not quite as jovial, but still, all was fine.
Lucky us, we were there when Ivan had everyone on pins and needles, but thankfully missed us.
I think Disney is probably more prepared than most: it would be difficult to convince people to visit if they were not.