Not to be "that guy," but the celebration is of the winter /solstice/, not equinox. Just wanted to clear that up for anyone unfamiliar reading your post.
Also, I wasn't clear if you meant it this way, but the Yule Log was already a pagan tradition, and was not added by Christians but rather adopted by them.
Merry Solstice! :)
As is tradition, the American form adds its own ideas consistent with the national culture: submarine advertisement for coca cola, consumption that has a large affect on retail, and partisan politics.