Its best to bring your own, we have a pretty lightweight stroller that is easy to carry around, not as easy as an umbrella but lose enough, also has a rain guard.
The Disney strollers are more trouble than they are worth, for us we go to multiple parks in a day, plus having to return the stroller getting a voucher to get one at another park is annoying.
Also the strollers are this hard plastic and not very comfortable for a kid, but you know kids once they are tired they will sleep anywhere.