It all depends on the school. Son played in the ACC. Pitchers at his school were expected to be in throwing shape as soon as school started. As soon as fall practice started they were all pitching in scrimmages. Even after fall practice they continued to throw, lift, etc. The only actual shutdown was during exams. They were also expected to be in pitching shape when practice started back in January, so they really could not shut down in December. Son would come home for Christmas break and head over to the local JUCO to long toss. JUCO pitching coach was amazed because he had his guys shut down.
After the college season was over it was off to summer ball, and then start the cycle all over again. The only real shut down time that most of them got (unless injured or overworked during the D1 season) was a couple of weeks around exams, and maybe a week or so after summer ball ended.
In my opinion, this is one reason why arm injuries are common in college ball.