I only had time for two yesterday, but they were both excellent suggestions. Connie Backus Yoder suggested "The Holly and the Ivy" in the style of Bach. For this one, I took something like the accompaniment figure from the cantata setting of Nun Danket and then just played the carol melody adjusting as necessary.
Austin White gave the diabolical request for "Christmas Time is Here" in the style of post 5th sonata Scriabin. That's a language that I could imitate, but it would take more thought and time than I am willing to give right now. I did do an OK Scriabin 4th sonata style rendition though.