Welcome to planDisney, Heather!
I am so happy that you stopped by with this question. I have spent time at moderate and value resorts lugging things back and forth from our room to the car, and a wagon would make that so much easier!
The official answer is....it depends. If you are staying at a hotel like
Disney's Contemporary Resort, where you must enter the lobby to get to your room, then you would not be allowed to bring your wagon to shuttle your things.
If you are staying at a resort with direct access to your room from the parking lot, like
Disney's Caribbean Beach Resort, you can use your wagon to shuttle your things back and forth.
I will say that depending on which resort you are staying at, and the number of people in your party, a wagon may take up valuable floor space, especially if you are also traveling with a stroller. If it were me, I would try to find a luggage cart once we arrived to get us to the room, or take advantage of Bell Services.
I know you will have a wonderful trip, Heather.
See you real soon!
Sarah B.