The closest thing to a Christmas song from anyone in the Genesis family is this contemporary jazz take on “Little Drummer Boy” by Daryl Stuermer, the band’s on-stage second guitarist and bassist. (At least until Steve Hackett played on Chris Squire’s 2007 Christmas album.)
In fact, A GRP Christmas Collection is one of my overall favorite Christmas albums, with great contemporary jazz interpretations of many well-known songs, and Daryl’s contribution opens the collection.