Congratulations on asking one of the most controversial topics on the dis boards.

LOL For some reason people have VERY strong opinions about this. My favorite responses are from people who don't have kids or haven't taken a child to the park since before the new millennium.

And before someone takes that personally - I haven't read any of the responses above.
Do whatever works best for you. Everyone has different kids, different ways of touring parks, different lengths of trips, etc. No 2 families trips are alike. We just returned last week from WDW with our 5 & 7 year olds. We had 6 park days of being there at rope drop and were in the parks for an average of 8-10 hours a day (after subtracting out of park breaks). We averaged around 6 miles of walking per day. My 5 yo definitely needed a stroller. She walked for 2-3 hours at times some days, but there were others times when she really needed a stroller. My 7yo did not need a stroller. He's a fit kid who doesn't complain, and only got tired on our very last night. He could have easily ridden in DD(5)'s stroller at any point and he just didn't want to or need to.
But, you know your kid and touring style best. Do what's best for you. You can always
rent a stroller after you get there, if you find you need one. Can rent from WDW or get a last minute rental from one of the local companies.