When my kids were young, we preferred to use our wagons on many family outings.
Places like parks and zoos were definitely easier to navigate with a wagon.
So, you may think that a wagon would be perfect for Disney World, too -
Wagons (along with anything that can be pulled behind you) are not allowed.
The fact is that pulling things behind you is dangerous and tricky when there are lots of crowds. It makes a lot more sense to navigate the crowds pushing something in front of you (where you can see it) rather than behind you (where you can't).
Most things that you can push in front of you ARE allowed - so strollers (definitely) and I've even been seeing some wagon-esque-push-in-front-of-you-thingys pop up in the parks. And, as long as they fit Disney's size regulations (36″ x 52″) they are allowed, too.
Want more information on stroller options? Check out our stroller guide.
So - what happens if you show up with a wagon?
Well, they won't be rude about it but they won't let you in. Usually what happens is they offer to hold it for you at the front and provide you with a rental stroller, instead.
Now, as soon as I say that somebody is going to say "but I saw somebody with a wagon that had a rolling cooler connected to the back like a train" and I have no doubt that they did.
But that is definitely the exception, and not the rule.
I personally don't think it is worth the risk. It's much easier to be prepared. So, leave the wagon at home and bring the stroller instead.