Your deluxe resorts get all decked out starting from Thanksgiving time; it's neat to take a ride on the monorail and visit the Polynesian, Contemporary, and the Grand Floridian. The Grand Floridian has an orchestra in the lobby balcony doing Xmas music sets. There's a piano player on the main floor doing the same in between the orchestra's sets. There's a full size ginger bread house there where you can buy gingerbread cookies. Their Christmas tree is wonderful and Santa comes out to the lobby, too. Even though it's not exactly a Christmas thing you can do afternoon tea there, as well.
The parks have character greets that are Christmas oriented. AK has a Christmas version to their parade. Epcot has Christmas storytellers, who explain the traditions in their particular culture. There's a Christmas version to Illuminations fireworks in Epcot. As mentioned, the Candlelight Processional is a real favorite; I recommend the dinner package for this event; it gives you guaranteed and reserved seating for the show (based on you getting there on time). HS has Osbourne Lights which are sychronized to music. MK has their special party (you pay extra for this activity). MK's castle is specially lighted for Christmas; the castle looks like icicles all over. Many of the special events mentioned here take place in the evening.
There's a special tour you can take that costs extra about the Christmas Holidays at Disney World. You go behind the scenes for this tour. When we did it we got a special ornament to take home.
There's enough Christmas going on at the World!