Hi gmeyer,
I have always considered "Papa's On the Housetop" to be a novelty song, though an unusually well-crafted one. I think the whole point of the song is how perfectly the lyrics scan with the rhythm of the melody and the melodic riff upon which the song is based. It's really kind of a blues patter song, like some British music hall songs or some of those of Gilbert and Sullivan. Other people might hear it differently, but I certainly don't see any deep inner meaning to it--it just seems a carefree, funny, happy song to me. And there is certainly no through storyline to the lyrics.
All best,
Johnm