Hi Kristi!
Hmmmm, good question. I can't recall ever seeing children in wagons at the parks. Then again, I'm sort of "in the clouds" when I'm at Disney, so a few things are liable to pass right by me without me ever noticing :-)
But I can say this: The double strollers at Disney you can rent work VERY VERY well!
The last 2 years we've rented Disney's double strollers. Last year, my son was 2 1/2 and daughter 6, and the year before 18 months and 5, respectively.
The strollers have a lot of size, and both were able to fit in the stroller comfortably. The latches were good, so my son wasn't slipping out, and they generally fell asleep by just leaning on each other, resting against the back of the stroller (Can you say, Perfect Camera Moment?)
So I'd say, give the double stroller a shot. It worked great for us.
And have a great time!