Last year, I read a similar stroller thread prior to a WDW trip with DSs, then 4 and 6. We have been to WDW each year since DSs were 1 and 3, and each year we had rented a double stroller. DSs had quit riding in strollers when they were 3 and 2 (everywhere except WDW), and wouldn't be caught dead in one at home.
Anyway, in the thread, a mom had commented that her similar age kids were physically fit, active kids, and that they didn't need a stroller at WDW. In spite of some concerns about where we would put all of our stuff and would we end up carrying DSs everywhere, she inspired me to try WDW without a stroller. I told DH that we would rent if we needed a stroller but I wanted to try not having one.
Being stroller-free was so liberating! We had a wonderful trip. All of us quickly realized how much time we had spent parking and finding the stroller after each attraction or area of attractions. We rode and saw significantly more attractions with the extra time. We could walk through any crowd and not worry about bumping anyone with the stroller. DSs never asked to get a stroller and never complained about walking. It was so obvious to them that they were getting to do more without a stroller. DH did carry younger DS twice, once from the back of AK to the exit, and after Illuminations from the World Showcase to exit Epcot, only because of the crowd or we needed to catch our plane. Did I mention that we tour commando-style, and stay at the parks all day? If we need a break, we sit and have a snack or see some shows.
What about all of the stuff to carry around? Well, we decided that DSs didn't need an extra outfit, either they wore a shirt that was a little dirty by the end of the day, or in an emergency, we bought a souvenir t-shirt, which we would have done anyway. I carried a small backpack with wallet, camera, film and a water bottle (we didn't need 4 bottles since we share all of our germs as a family anyway), and that turned out to be plenty of stuff and all that we needed.
I understand that for medical reasons some children need a stroller. However, for healthy, active children over the age of 4, I highly recommend trying WDW without a stroller.