I used my Amex for our first trip to disney and didn't have a problem. Even got a neat little pin for using it at check in. I did not let Amex know of our trip beforehand.
Now another one of my cards (Associates~now is CapOne) did stop my charging privelages in Orlando once, b/c we had used the CC there before and all of these charges started popping up and my CC company thought it was stolen. After being humilated in line at IOA and a call to the company we got it straigtened out. It was kind of reassuring to know that they were watching out for me, though. So I always let my CC company know before we go anywhere to expect charges from out of town to prevent any possible problems.