Long long ago, in ancient days when men were real men and sheep were real scared, i.e., when I was a kid (the '50s), people in movies and TV would actually call Santa "Santy". If you Google it, it'll tell you that this is largely an Irish thing. Indeed, here in New England, I've heard the Irish use the term...but not after the 1960s at the very latest. I thought it was just a quirk of their accent.
Apparently not, because on TV, gangsters, other so-called tough guys and even little kids (for some inane reason - like in this song) would also call Santa "Santy". Clement Moore didn't call him "Santy" in "A Visit From St. Nicholas". My parents didn't tell me to write a letter to "Santy" Claus in 1949. What the hell was going on? It turned out to be just quirks of the Irish and the entire early 20th century. Go figure. Try saying "Santy" these days and they'll tell you, "You're drunk; go home!"