No wagons, no rolling coolers. If it drags behind, you can't use it. Also, if the parks are crowded, they sometimes make you leave your honkin' big jogging stroller at the front gate and use a rental (for free). You can wipe out a small country with some of those jogging strollers.
Strollers always have to closed up to ride on the buses. On the monorail, if it is full, they might make you close up your stroller. Boats, you can usually keep the stroller opened up and in use. Except for the smaller ones like the little one from MK to GF or WL to CR.