Classes stop usually for a two week period from before Christmas until after New Year. I taught at Sill and students were encouraged to use leave or at the least take pass. For those without leave the duty day was execute PT and then report in for the morning. Students might help with menial tasks like cleaning supply or publication rooms. Everyone dismissed at noon. Christmas and New Years are both 4 day holidays as well.
This half day model is pretty typical for most active units I have seen as well.
Yea, pretty much everyone not deployed goes on block leave for about 2 weeks. This includes BOLC, Basic Training, AIT, and environments such as those. You don't have to take leave during this time and you don't have to take the full amount either, it's just a set aside time for people to take leave this time of year.
The Army pauses training during the holiday, called Exodus...on or about 22 Dec through 3 Jan. Here is a brief explanation for the Future Soldiers that are shipping out in September and October. The Army shuts down its Training operations for a 10 day (or so) period at Christmas. The primary reason for "Exodus" is so Drill Sergeants and Basic Training Staff members can spend Christmas with their families. So this results in a break for basic training recruits also. If you are "lucky" enough to be attending Army basic training during the Exodus period, you will be given a choice: (1) You can remain at basic training and be assigned to do details during the 10-day period, or (2) You can take leave and go home. Any leave you take comes out of your leave entitlement (30 days per year, soldiers earn 2.5 days a month). Additionally, you have to pay for your own transportation home and back to basic training at the end of the Exodus period.