I wouldn't go to Disney without one!
We have a double stroller. And I still stand behind that statement.
Yes, it is a bit bulky, but wow...it can hold lots of stuff....and the kids get tired and we can just push them along. We can put a cooler bag with juice, water, soda, snacks in there, diaper bag, cameras, etc. I can guarantee you that a 2 or 3 Year Old, and probably a 4 and even 5 year old will get tired partway through the day. Of course it depends on the child, but I've seen enough kids saying they are too tired to walk and making their parents carry them to know that I would not want to be without one!
We can now drive to Disney, but before we moved last year, we travelled with it on the plane. Had to take kids out to put stroller through security, but then loaded them back and wheeled to the gate. The airline put a gate check tag on it, and we wheel down the walkway and fold up next to the plane door. They load it onto the plane, then it is waiting for us when we get off the plane. Put the kids back in and wheeled them down to Baggage Claim.
We specifically went to Polynesian last year because we had the stroller and wanted to be able to roll it onto the monorail.
This year, we went to BCV so we could roll it directly into Epcot, onto the MGM boats, or onto the Epcot Monorail to get to MK.
It will be a little more of a pain for this trip since we are staying at the ASMo for the first 4 nights. We will have our SUV and will either drive to the parks, then take the tram to the front, or just take the bus. Either way, we won't be able to pack up the stroller first since it will need to be folded up. We will then stay at Boardwalk villas, so it will be easier.
We also have a BackPack that my wife or I use occationally: