Christmas All Year Community

I ask this because my sister and I constantly argue over this topic. She says that there are more songs about Jesus' birth than about snow, snowmen, reindeer, and Santa. I tell her it's the other way around because those 4 things are the first things we think of when someone mentions the word "Christmas".

What do you guys think constitutes a Christmas song? Does it have to be about Jesus' birth or can it be about the Big 4 (snow, snowmen, reindeer, and Santa)?

Both Jesus and the big 4 are in Christmas songs. But they are 2 totally different Christmases. One Christmas is celebrated by Christians (Jesus' birth). The other Christmas (commercialized: Santa, Snowmen, Reindeer, Snow, etc.) is celebrated by a wide variety of people including Christians.

Just like Easter.
Christians celebrate the death, burial, and resurrection of Christ Jesus.
And a wide variety of other people, including Christians, celebrate Easter with the Easter Bunny, Candy, Easter Baskets, etc.

If I had to guess. I would think there are more songs about the commercial side of Christmas right now. But that is just a guess.

So we can only call it a "Carol" if it has to do with Jesus' birth, so to speak?

I mean, there are a lot of Christmas Carols books that have a combo of both Nativity songs (I'll use that term from now on) to "Big 4" (Santa/Reindeer/Snowmen/Snow) songs. Would a book title like that be misleading?