That is right. It must have been last Christmas when people were talking about non-Christmas Holidays around this time of year that I encountered my first reference to "Dies Natalis Solis Invictus" which is the unconquered sun's birthday. I just added a Felix to it. (I saw people using Felix in Merry Christmas translations, so it seemed a good word to pick.)
And then after posting I randomly panicked, assumed the words were all in the wrong cases, double checked the declension of each of them, and thought I found that all was as it should be, but in fact I somehow missed the fact that I wrote Invictus when I mean Invicti. I got that right when I wrote it elsewhere.
It is Latin.
Like, "Merry Christmas," it isn't actually a sentence (there's no verb), but other than that I'm reasonably sure it's a good Latin. Dies (Day) is the subject of the non-sentence, felix (happy, lucky, blessed, fortunate) modifies it. Natalis (birth) is genitive, so it is the day of the birth
. Solis (sun) is also genitive, which makes it the birth of the sun
. Invictus is movie with Morgan Freeman and Matt Damon, it's also the name of the poem that movie is named after. Invicti is what I should have written, it's an adjective agreeing with solis. So when someone asks, "What kind of sun?" you can say, "The unconquered
Anyway, the sun's birthday is apparently December 25th according to at least one cult in the Roman Empire.
If this post seems a bit disjointed, it's because I went out to spend Christmas with my family in the middle of it.