Yes, everyone goes home at the end of exam period, and players (although I'm mostly familiar with pitchers) continue their preparation for the spring season over the holiday break. In the Northeast, the pre-season starts with travel down south in mid-February, so pitchers are definitely starting to throw after Thanksgiving. My player would shut down from early October to Thanksgiving and then ramp up to speed by mid-February. The team would return about 10 days early to campus for regular workouts. Southern players probably have a different schedule though.
Most players also have a regular workout facility for times when they are home or out of season. Your HS player probably knows where the college guys and minor leaguers work out. If not, ask around the travel team circuit and someone will point to the right place . . . since these places cater to young college and early pro players, in my experience, they are not overly expensive. Beware the places that just give expensive lessons.
Finally, my player always pays for workout plans from his favorite trainer over breaks. Yes, they are probably between $100-150 every 8 weeks, but he believes that a customized plan is totally worth it. Now, some college trainers do provide their players with these plans; however, if the trainer also works with the football team (which is often the case at schools with smaller programs), then these plans might not work as well for pitchers simply because there is too much emphasis on biceps, etc. I'm not sure if position players have custom plans, but someone on this board will definitely know.
Maybe more info than you asked for, @Brensdad, but I hope some of it is helpful.