Springsteen's version of "Santa Claus Is Comin' To Town" is borrowed from Phil Spector's arrangement on A Christmas Gift For You, which is one of the greatest holiday albums ever.
It's mostly traditional standards and carols done up in early 60s Wall Of Sound arrangements, but here's the one original song, which has been covered by everyone from U2 to R.E.M. to Death Cab For Cutie , but Darlene Love's original version is still the gold standard for "Christmas (Baby Please Come Home)".
She's been playing it on Letterman every year since he was on NBC.
Darlene Love just made the Rock & Roll Hall Of Fame, which is kind of surprising as much as I love that song (and "Marshmallow World").