The Meaning of SHAWTY
SHAWTY means "Young girl/woman"
So I think here "shawty with you" means that he woule like to spend the Christmas with the girl.
Yahoo answer for SHAWTY
It is a slang term that originated in the south. Shawty is the phonetic spelling of 'shorty'.
'Shorty' started out as a term that men used to women. Not offensive, but descriptive of man's dominance over women. The same way men used to call women "kid" (such as Humphry Bogart saying "Here's looking at you kid" in Casablanca).
Now 'shawty' is another way to refer to anybody, men or women. It is synonymous to 'dude' or 'man'..