It's not exactly a best or worst, but the most...awkward...Christmas song is likely, "I Saw Mommy Kissing Santa Claus". As an adult, it can appear perfectly innocent: We can see it as an attempt to be cute, with the wife kissing her husband, whose dressed up as Santa, or somehow taking on the role of Santa. But think about it from the kids perspective. The kid has two interpretations. Either Santa is dad, and the whole story of Santa is a lie, ruining Christmas for them, or they have to assume that there mother is an adulterer, cheating on her husband with a fat guy who is supposed to represent joy and happiness, not a homebreaker. Really, the song is not very well thought out. Granted, it could be about a single mother, but especially given the fact that it is a old song, no kid is going to naturally assume that. I bet that song has ruined a few childhoods.
A close second for awkward Christmas songs is the whole, "But Baby It's Cold Outside" song. Go into it imagining the guy as a sexual predator. Suddenly, its not so full of holiday cheer, is it?