They seem to range from classic big band and rockabilly stuff, to folksy shame-on-you-for-being-happy-during-Christmas stuff, to just plain weird stuff. The song I picked is probably closest to the last category. Before George Michael tossed aside Wham! like an old dirty rag, they recorded a Christmas song: "Last Christmas", a strangely smooth post-Christmas breakup song.
Personally, I think that breakup songs should be disastrous, petty, pleading things like Ben Fold's "Song for the Dumped" (warning: explicit) and Cee Lo Green's "Forget You", so I decided to record my own version of "Last Christmas":