Hi Ashley! I would have to agree with your kids that Christmas just wouldn't be the same if you didn't have a tree. We have spent a few holidays at Walt Disney World and we have always made sure we had some sort of tree.
In the past we have gone through
Disney Floral and Gifts. They have quite a few holiday things for you to consider from special hats to floral to full room decorations. If you do not see a tree or what you are hoping to find then please give them a call at 407-939-4438 and talk with one of their dream makers. They will always try to work with your needs and desires to make your vacation extra special.
If you are going to have a car with you then it opens up other options. You can visit one of the locate grocery stores, Walmart, or Walgreens and find a small tree on your own. Do not bring in a live tree and decorate with lights as this is a fire hazard. You can have the kids make their own decorations or buy some and let the kids finish the tree. Your budget will determine how you will like to finish the tree.
No matter what you decide a tree is simply a must for the kids. When we were there we actually took pictures of their gifts before we wrapped them and then took envelopes and put the pictures in those. We wrapped the envelopes and had the kids open those on Christmas Day. It was a good way to prevent having to take gifts and when they arrived back home they had fun opening up the "real" gifts. They had Christmas morning twice!