Jim, there's a reason why "Over The River And Through The Woods" doesn't mention Christmas (or Santa, etc.). If you look at the lyrics you'll see that the song is actually about Thanksgiving Day, not Christmas. you'll see that the song is actually about Thanksgiving Day, not Christmas.
At least that's true of all the versions I've seen.



Big Al Whittle, you asked "What's wrong with Christmas, why not mention it - if that's what your song is about?"

Well, because sometimes the word "Christmas" doesn't fit with the rhyme scheme, the meter of the lyrics or even the story.   (E.g., if your song is about the night Jesus was born, there was no such thing as "Christmas" at that time.) "O Holy Night" doesn't mention the word "Christmas," nor do most of the most familiar Christmas carols.