Hi Jennifer!
Thank you for bringing your question to the Disney Parks Moms Panel!
This is a question that I see frequently, and is often met with some confusion. According to the Walt Disney World Resort Park Rules, "Any trailer-like object that is pushed or towed by an Electronic Conveyance Vehicle, wheelchair or stroller, or pulled by a person, including wagons" are prohibited from the parks. You can find all of the
park rules and restricted items here at this link. As the wagon trend has grown, there have been some sightings of them in the parks. However, they are not allowed in and are likely to be turned away by security.
You can find information about
stroller rentals at Walt Disney World here. When my boys were little, we always rented strollers at the parks. It kept us from having to drag one there, and they were roomy, with big wheels for easy maneuverability.
I hope this helps! Please let me know if you have any other questions.