A student asked over the holidays, “Mr. Thomas, How do I say Merry Christmas and Happy New Year in Latin?”
Here is my reply:
As for Merry Christmas, I would go with: felicem natalem Christi!
It’s often helpful to look at the same message in other Romance languages.  And, just for fun… Esperanto.
Spanish: Feliz Navidad!
French: joyeux Noël!
Italian: buon Natale!
Romanian: Craciun Fericit!
Portuguese: feliz Natal!
Esperanto: feliĉan Kristnaskon!
Happy New Year – Felix annus novus. 
Spanish: Feliz año nuevo!
French: bonne année!
Italian: felice anno nuovo!
Romanian: an Nou Fericit!
Portuguese: feliz Ano Novo!
Esperanto: feliĉan Novjaron!
Hope you are having a felix annus novus so far!
Dwane Thomas