My DS7 normally doesn't ride in one at home, but halfway through our vacation he normally gets tired and wants to ride. I take my umbrella for the first part of the trip for DD3, then by the end I'm renting a double for both of them.
I could make him walk, but I know he gets less tired if he can ride (especially if he asks to ride in the stroller). It saves my sanity by letting him ride and not get quite as tired. He normally walks around MK (we go there early in the trip), but by the time we get to MGM and esp EPCOT, he's toast.
It really is about what you're kids can handle. Just keep in mind that in WDW kids get more tired, even if you keep them on their regular sleep schedule.