Chances of seeing the aurora at Thanksgiving or Christmas are really about equal. The key factor is the weather and solar activity. The best viewing that time of year is when it's bone-chilling cold and clear. Wear lots of layers and good insulated boots. The key to staying warm is toasty feet.

Here's a link to the UAF Aurora Observatory aurora forecast website. You can check out a 28 day solar activity forecast. High activity means lots of multi-colored Northern Lights.
http://www.gedds.alaska.edu/AuroraForecast/

As to the issue of driving from Anchorage to Fairbanks during the winter, I hate it. Even if you get up to Fairbanks, you may not be able to get back to Anchorage when you want to because of road conditions. But, if you decide to do it, you can check out weather and road conditions on the Alaska Department of Transportation website.