Funning up other songs is MY own special category.
‘O Christmas Tree’ gets a fumble with “My Christmas Cards Came Back to Me” by Carol Denney. Humor, if you need to know.
Billy Joe Duprix gets off track with his ‘Rudolph’ run “Christmas Cards.” They’re credit cards, these cards. That’s something else. Sorry.
While we’re tangential, Alan Sherman has a parody he never quite released: “Christmas ’65 (Draft Cards).” It starts as ‘The Christmas Song’, then gets to commenting on all of last year–like a family letter for the holidays, now that you mention it.