The question I think of is if the tune has to be depressing or if just the sentiment of an up-tempo song fits the bill for depressing. The Kinks tune "Father Christmas" (I think is the name) fits that bill for me. "Santa Baby", for it's similarly shamless materialisim. "Grandma got run over by a Reindeer" for obvious reasons (Surprised I did not see it mentioned yet)
As for playing it straight "Ill be Home For Christmas"... if only in my dreams... is rather melencholy.

As for Stan Rogers, yup! He also has a spectacular bummer of a song set in winter (Perhaps around Christmas) in
"Harris and the Mare"
I do like much of Stan's music.
As for the "Heroic Stan" stories of his death I think they are just the stuff of legend, would love it to be true but I think it is not.