My answer is from an American English perspective.
In the U.S., the word holidays in its plural form is rather uncommon, except when referring to the holidays around Thanksgiving (late November), Christmas, (late December), and New Years (early January). Sometimes the week between Christmas and New Years is referred to as "the holidays." It's a time when many businesses are manned with "skeleton crews."
In those cases, I think the preposition of choice would typically be during or over, not on or in:
I am going to clean my room over the holidays.
I am going to Europe during the holidays.
I find the expression "my holidays" to ring a little awkward; in the U.S. at least, we tend to favor expressions like "my vacation" or "my days off" instead.