Although I was not there, and I did not have a reservation to go during that time frame, I had co-workers who became stranded at a Disney Institute seminar. They experienced wonderful Disney hospitality and magic!!!
They were unable to leave for several days - remember the airports were closed. Disney aided them in every way possible with housing and they were very accomodating about rooms. They tried to leave the 1st day the airports re-opened, but they could not get on flights (to Seattle). They went back to WDW from MCO and they were accomodated. I believe if my memory serves me right, that they paid a reduced rate on the room, versus many other establishements who were noted for gouging stranded folks. In their opinion, Disney was most kind and helpful. I wish I remembered more details, but it has been awhile.