I've CDd through three kids and all kinds of travel. The only disney trip we've taken with kids was to
DisneyLand, but we continued to use cloth on that trip. I washed in the hotel washer and dried in the hotel dryer. I generally use thinner fitteds with a separate soaker or stacked flats for travel, because thicker fitteds, AIOs, and prefolds tend to take forever to dry. If you use flats, you can also consider what I ended up doing on a cruise we took (non disney despite my heavy lobbying, i was not the one in charge of this trip) - I washed the pee-only diapers (in the sink, actually, because this ship didn't have coin op laundry), and threw out the poop diapers. I brought enough flats, and they're cheap enough, that I felt OK doing this. I ended up spending maybe 10 minutes a day on cloth diaper related tasks, which I didn't think was too bad.
All in all, I didn't find Disney with cloth to be any different from any other activity with cloth.
If you decide to switch to disposable instead, be sure to use the disposables you plan to use on your trip while you're still at home so you know what to expect in terms of blowouts and reactions. I had a good friend switch to disposables the day of a big international trip, and discovered on the airplane somewhere over the Atlantic ocean that her daughter was severely allergic to the disposables she brought.
