That is the time of year when the weather is really changing to winter. I've had Thanksgiving trips that were balmy (mostly) and others that were snowy and cold (single digits at night). You will have to watch the weather before you go.
The trail will be fairly busy but more so south in the Standing Indian area and north in the park. The biggest concern is that is rifle season for deer hunting and so you need to be careful and wear plenty of orange. That is why we usually go to the park during Thanksgiving where there is no hunting.