If you order the Christmas tree from the WDW florist, you just have to get it picked up and taken back to the Front Desk. The Florist will pick it up and ship it to you.
At the Grand Floridian, you simply take anything you want to the Front Desk, unboxed, and fill out a shipping form. It will be taken to the Business Center and boxed and shipped by your choice of carrier. Other resorts with Convention services probably perform the same function. At the Polynesian, you need to put it in a box and take it to the Front Desk and they will ship it by UPS or FedEx. I believe the other Deluxe resorts are the same.
If you are staying at a moderate or value, call them before your trip and ask these questions.