The parks have both single and double strollers, and if you rent for several days, you get a $2.00 per day discount. (They give you little cards to show, and they are good all day, even at more then one park. - It also saves on standing in line again.)
They were roomy, and my 5-year-old much preferred them to walking. They varied a little by park, but all had some sort of shade and mesh pockets to hold water bottles, etc. The MGM/Disney Studios ones were an older style, and didn't have quite as big a pocket, if I remember correctly, but were still OK.
Watch what you hang off the back of any them, though. If it's too heavy, they can tip when the child gets out.