Hiya, Bridgette! Boy oh boy, are we glad you stopped by today to ask your question.
There is a pretty strict set of
property rules when you are visiting
Walt Disney World. These rules cover a lot of territory - everything from supervising children to the types of floatation devices you can use at the resort pools. You'll notice the list of rules has a section for prohibited items, and on that list, about halfway down, you will see that wagons are prohibited at any
theme park and
water park. This includes wagon-type strollers as well.
I know this can be inconvenient, but if you were using the stroller for children, there are some awesome
stroller rentals at each of the theme parks. The rental counters are located at the entrance to the parks, so you won't have to go very far to snag one. I like the double stroller size, even if you just have one child because it gives the extra space to spread out and collect souvenirs.
If you needed the wagon to carry the things you'll need at the park throughout the day, as opposed to having it for kids to ride, you'll find
locker rentals available at each of the parks. If the things you are carrying are ones you won't need in a hurry, you can place your things in the lockers and just return when you need something.
I hope your upcoming visit is magical and memorable, Bridgette!
Anna