Yes, training does take place over the holidays. Most of the PC's are pushed off because that requires company check airmen. But regular ground classes and specifically PT's are usually on going because the Training Center instructors have to be there..working.
When I did my New Hire training my class, and the class that started before and after mine, did train over Thanksgiving and Christmas. Granted we did get those days off but we trained on the days before and after.