We went this last Thanksgiving and it was busy, but I would not say it was crazy. I guess it is all relative though. Since we go to DL and WDW regularly, we don't stress over having to see everything. We were there the entire week, including Thanksgiving day, and we never felt it was crazy busy. We were expecting a lot worse.
It really all depends on your touring habits. We go to the parks early and leave early. Sometimes we go back late in the evening. We walked onto several rides through out the week and used FP's. HM and IASW was walk on everytime we past by.
SM and SpM were pretty busy most of the time and the FP's were all gone early in the day. At DCA lines did get long for TOT, TSMM and CS during the middle of the day, but morning and early evenings were not bad.
I was also able to book Ariel's Grotto and Blue Bayou with in a month of our trip and got the times we wanted.
If the only time you can go is during that week to see the Christmas decorations then I would go, but if you can wait until the week after Thanksgiving, then that would be a great time to go. We went once the week after Thanksgiving and it was awesome. Really quiet and slow paced.