For a 3-day trip with an active 4-year-old, I see no problem. My daughter's first trip to WDW was for 6 days as a "strollerless 4-year-old," and she did beautifully.
We (DH, me our 4-year-old daughter and 6-year-old son) would arrive at rope drop, pound the pavement for 4 hours, and then after lunch go back to our hotel for a 2-3 hour nap/rest period. Then we'd return to the parks around 4pm for another 4-5 hours, at a more leisurely pace. We took plenty of snack and bathroom breaks throughout the day, and the kids had no trouble keeping up. To the contrary, DH and I were usually having to rush to keep up with them! I think the nap break (and reasonable bedtime - we only stayed up late the last night) was really essential to keeping everyone refreshed and energized, and we were so glad not to have to deal with the hassle of pushing a stroller around.
I think the parents of 4-6 year olds who swear by strollers tend to be the "touring commandos" who are engaged from morning until late at night without any significant breaks, "kitchen sink club" folks who like to use the stroller as a mobile locker, or else they simply have kids who are a little small for their ages, or who have other physical issues that prevent them from walking a few miles in a day.
I also second
@Efig8594's advice on footwear. Good sneakers and/or hiking sandals (e.g., Keens, Tevas, etc.) are a must -- no skinny flip-flops or plastic princess shoes. Like Lieutenant Dan told Forrest Gump, the first priority is to take care of your feet!
