My family recently returned from a couple very rainy days at Disney. We bought the Disney Mickey Mouse ponchos, (thicker variety) and thought they worked out so well, we packed them and brought them home. They wipe down very easily for re-use, and though we had a stroller to throw them in the bottom of when wet, they didn't bother us when the rain stopped.
I saw a couple good tips on a board somewhere, maybe allearsnet.com, that mentioned wearing sandals instead of sneakers because they dry out more quickly. I wouldn't sacrifice the comfort of sneakers myself, but have never tried teva like sandals. One guy who no matter what the forecast is, or what time of year it is, says he always brings rain gear, rents a locker first thing, and puts the rain gear in the locker, change of socks, shoes, ponchos, umbrellas, whatever. Then he doesn't have to lug it around, but it's there if he needs it and he doesn't have to got to the expense of buying ponchos in case of unexpected weather (although I don't know how much lockers cost). I guess if you expect afternoon rainshowers, it may not be a bad way to go, since you wont have a stroller!
And my sister-in-law thinks the heavy ponchos are so great that she always brings them and makes her family (twin 5 year olds) wear them on wet rides like the river rapids ride in Animal Kingdom. She swears it's saved her camera equipment, and headed off kiddie tantrums.
PS, have fun and don't worry about the weather. When we last went, it poured in the morning but we ponchoed up and went. It was cloudy all day in MK, but more importantly, it was EMPTY. The threatening weather kept the crowds away even though it never rained from 9 am on, and we never waited in line. Truly magical.