Well back in my day, all short 12 years ago, if you went to boot during the holidays, you stayed at boot during the holidays. Don't know if you exchanged gifts or anything like that, but i am pretty sure they give you a special meal during that time. I don't think that you can leave base during holidays(least you go out in town and eat some good food and spoil that meal plan they had you on) and not sure if you can have visitors. You will not get leave between Boot and A school, you will fly directly to Charleston and there will be a duty driver to pick you up. If you are in A school during the holidays, they will stand down and all but force you to take leave. When I went through, we had 2 weeks of christmas leave and came back, graduated A school and got 2 more weeks of leave a mere month later. You will get two more weeks between Power School and Prototype, some of which will be taken up getting set up in a new apartment(unless you are smart and during your few precious free hours you work on getting everything set up while you are still in school, such as utilities, apartment searching, and figure out what to do about furniture). You can take leave during Prototype but ONLY if you are fully qualified. There is NO standdown period during the holidays for Prototype. Best you can hope for is a couple of days off during your normal shift week, and that is only if you are either qualified or very far ahead of the curve. After Prototype, you will usually get close to 30 days of leave if you want to take it to get to yoru next duty station, depending on operational requirements of your new ship(such as if they are getting ready to deploy, they might not let you take all 30 days).
While on the ship, leave is a whole other matter. Yes you can take leave, but it isn't as easy as in school. YOu have to find people to cover your duty, can't miss underways, and most of the time you have be supporting the watchbill in some way prior to taking leave. Holiday standdowns are also different on the ship, which is what BeerCourt is getting at. They generally let half a department go on leave for a week and then the other half. Most of the time it is Duty section only work days(means you don't have duty, you don't come to work) but due to half of the people being on leave Duty rotation usually gets cut to half as long as it was. For example, after my first deployment we were 8 section duty, duty section only. That is because no one took any leave. We came to work once a week. If people took leave, we would have been 4 section Duty and would have had to come to work once very 4 days and burn leave.
Hope that clears things up for you, or did I just throw in a bucket of dirt???