In Harry Potter, what does Christmas mean to the wizards?

Question stolen from @genkan :)

There’s no doubt that Christmas is a significant celebration in the wizarding world. They have a break for it, and many traditions (decorations, ugly knitted sweaters, etc.) are the same as with muggles. The main difference is the absence of Jesus and Christianity. I can’t remember if Santa Claus is ever mentioned either.

So far I can think of four explanations:
1. Jesus was a wizard of historical importance, and they celebrate his birthday without mentioning him at all
2. Santa Claus is a wizard, and for some reason a tradition has developed around gift-giving in December
3. They are celebrating Yule, but treating it like a muggle Christmas
4. They saw muggles celebrating Christmas, thought it was pretty cool, and adopted the parts that they liked en masse, and it became one of the biggest (if not the biggest) celebrations in their calendar

Obviously the search terms “Harry Potter” and “Christmas” aren’t turning up anything like what I want to know. Has J K Rowling said anything about this? What do you guys think?