I went to school in England in the time frame that the books are set in. I didn't go to a boarding school, let alone a magical one in a remote part of Scotland, but I was in Cambridge which has a high density of fee-paying boarding schools and their terms were much the same as ours (if slightly shorter).

The whole academic year in the UK is structured around three big holidays: Christmas, Easter and summer (the longest one). Hogwarts follows this, possibly because it makes sense in terms of fitting in with the Muggles (wizarding kids would be home from boarding school for the holidays at times which suit the expectations of the Muggle neighbours and thus reduce suspicion).

The reasons for the UK's school system stem of course from Christianity, which is the established religion in England and the religion of the majority of the country who hold a religion, and more so in the time of the books than today. These days we're one of the most atheist countries on the planet (even if people say they're Christians, observance and actual belief are pretty low), but we still celebrate Christmas as a big winter festival - with many elements everyone enjoys these days (including those of other religions) being those adopted from the midwinter festivals preceding the arrival of Christianity which were borrowed as a framework for the celebration of Christ's birth (just like the spring/fertility festivals became Easter, and we retain that imagery in Easter eggs, chicks etc.)

The summer holiday is from farming, giving the children time away from school to help with the harvest and all the massive activities required on a farm during those most productive months of the year in the northern hemisphere.

So all Hogwarts is doing here is expressing the UK's primary cultural heritage. There are clearly students present from other religious backgrounds, but there's no fuss made in the text about anybody actually observing any religions - none of the students who might be from Christian families ever mention going to services or praying or anything like that, and we don't see the Patils (who we might guess are Muslims descended from immigrants from Pakistan) praying five times a day. Rowling seems to have decided to just not mention that side of life in the books - Harry clearly isn't religious, so maybe it's just not important to his worldview and so doesn't get mentioned from his POV. Or the books just reflect the nature of day to day life in the UK - if you're not actually religious yourself - which the majority of us aren't - you mostly just don't think about it.