There are trams that will take you to the main entrance. A 4 year old would be fine in the morning walking until you got in the parks - you're not talking too far of a distance. The problem with us has always been at night. "My legs hurt!" "Daddy, carry me!" They are tired, and it's hard to give up that stroller they've been sitting in all day to go stand in a long line to get on the monorail or wait for the tram to come pick you up. It's kind of a toss-up. We stay on-site, and you usually are talking a big walking distance from the parking lot to the hotel room, so I like having my own. We don't have to make any mad dashes to the tram as we ride the buses to the parks. But off-site, you're usually going to be able to park closer to your room. And it's possible right when you come out of the park the tram may be just about to leave, and you'll be making a mad dash to get everything out of the stroller so you can make that particular tram. Just kinda gotta weigh your options. Is it going to be a pain in the airport? Are you willing to put up with a little bit of inconvenience getting in and out of the parks?
We took an umbrella stroller on one trip with my DD was 3. It worked great as it folded up quickly, but it had no storage capacity. We now like to carry a small cooler, and I put my backpack in the stroller instead of carrying it. But if you're not going to have much to carry around the park, I would go that route. They're cheap, easy to pick yours out in the crowd, and you won't have the hassle of folding and unfolding a bulky stroller.