LOLThanks, Grinning Cat.
An acquaintance pointed out that the refrain is something of a soramimi -- lyrics "misheard" or interpreted as similar-sounding lyrics in another language. (Here, the original Latin is "Gaudete, gaudete, Christus est natus ex Maria virgine, gaudete.") It's related to mondegreens -- misheard lyrics staying within one language.
My first exposure to soramimi was "Oh Four Tuna", a surreal interpretation of "O Fortuna" from Carmina Burana. There are a number of versions on YouTube.
Another version: "Gopher Tuna"
Jaclyn Glenn and Eric Schwartz sing "Have Yourself a Merry Little Mythmas"
The lyrics are on the YouTube page. A notable bit:
"Lots of songs about Santa Claus
You can gather 'round and sing.
Teach your kids to believe in him
and they'll fall for anything."
I haven't written any song parodies in several years, but I think this could also be written as "Have Yourself a Merry Little Solstice." With a line somewhere about "Axial Tilt is the Reason for the Season...."