I’m from the UK and my partner is from the States. Every year she has the kids leave milk and cookies out for Santa, which I find odd because we left out sherry and a mince pie in my house. At the same time, we live in Scandinavia and I’m sure the Christmas gnome (julenissen) is unhappy about the lack of porridge.
In the states nothing says Christmas more than sugar cookies cut into christmas shapes and painted by the kids. I don’t know how prevalent it is these days, but when i was a kid, it was a big deal. And what do you drink while eating cookies? Milk. So yeah here in the states it’s very Christmasy.
My mom used to make like a dozen different kinds of cookies around Xmas, and as kids we would help decorate some of them, but ALL them were kinds of cookies she’d only make at Xmas time, so were considered Xmas cookies. To this day, the idea of making a kind of cookie that you would eat during the rest of the year for xmas, like a chocolate chip cookie, seems very wrong to me.