Depends on what you are looking for, the way the dates fall on a given year, and the weather.
Epcot is usually a hard stop right after Christmas. DHS will most likely keep the lights going til the 4th or 5th this year. MK might keep lighting the castle til then as well. AK parade would also typically stop at that point also. It's usually the first weekend after New Years when they stop most of the events. The decorations will come down at any point after they no longer have events going on. Last year MK was open til midnight on the 5th with EMH, we make it back to AKL to see them disassembling the tree. Any given resort can be completely stripped overnight. The parks might take 2 or 3 nights, but they will do it methodically.
But we have also been down there during a freak cold snap, that had them leave pretty much everything up til mid to late January. If you are arriving on the 4th, that may be your one shot to see the lights and the castle lighting, so I would plan on doing either of those (or both of them) that night if they are important. As your trip progresses, you will see things slowly change back to normal.