If the student is in dorms, the dorms will close. D3s have a specific number of practice days with coaches allowed, but the coaches can schedule those however they choose before the start of the season (i.e. in the fall, winter, etc.). At my son's D3, some years they came back 7-10 days early from winter break and were allowed into the dorms (I think it was most winter and spring athletes), some years they didn't come back early.
Regardless, players are certainly expected to keep up with their training over break on their own, especially pitchers who are on a ramp-up schedule.