Ha! Sure fooled me!

Is there any chance that the tune is at all "ancient," or that the song as a whole (lyrics/music) was somehow adapted from anything with a longer history?

I wouldn't have thought there would have been a "market" (any demand at all) for a pointedly non-Christian holiday carol anywhere in the English-speaking world in the late nineteenth century. I'm not aware of any neo-pagan movement (like today's) during that era.