We have a double stroller ( the baby jogger city mini double) for our two youngest, who are 2 and 3 yrs. We will absolutely 100% use it every day no matter what in the parks.
We also have a mac quest that we took with us in Feb as a "just in case we plan a really long day" stroller for our five year old. Thank God we did!!!

Our daughter hasnt used a stroller in at least two years, and was even embarassed at the fact that I would suggest she sit in a stroller in the parks. After the first day of touring, she practically begged for it!
And regardless of what people will tell you about overweight kids, etc.... you have to make your own choice for your own kids. Who cares what other people think? And my kids are all in the 30% percentile in their weight for their ages, so obviously the stroller isn't having any effect there!
As far as naps during the day, my kids need them and I can't sleep during the day if you paid me... so the rest stop in the afternoon is strictly for the kids. My DH learned on our third day that we could save sooo much time during the day by NOT taking the disney transportation back to the hotel for the kids for a nap (not to mention they usually zonk out on the bus and then you have three sleeping kids, plus two heavy strollers to lug off the bus!!)
So what we did was when it got to be their time where crankiness set in... we reclined the seats on the strollers and headed to a corner where there wasn't much commotion, got them a drink and chilled for about 15 minutes. All three of them were OUT by the end of the fifteen minutes. We then would pull up the shades of the strollers, make sure they had plenty of shade, and we'd push them around the park and enjoy the adult things we wanted to see, without boring the kids. After walking for a while, we'd stop and enjoy some ice cream by ourselves and relax in the shade until the kids woke up. It was a relaxing and we didnt have any hassle at all!! And who doesn't love to people-watch in disney? It's entertaining to see what some folks wear/do/act like in public
Bottom line, a stroller works for our kids, the oldest being 6 when we go back... and I would just say if the kid can comfortably ride in the stroller then you're good to go
