For an opposing view - We spent a week at WDW with our 5 year old twins the first week of April. I was sooo happy that for the first time in 5 years we did not have to manhandle 2 strollers all over the park! I have always hated trying to get through crowds without taking out someone's ankles or moving in a shop without knocking off some crystal goblet or something.
The girls did very well. The only time I carried them all week was to see the last Main Street Electrical Parade.
I would suggest, though, that you pay special attention to their feet. They are not quite old enough to realize the are creating blisters or hot spots until the are already bad. Good tennis shoes (or equivilent) with socks kept dry and on the feet are a must.
Mat