Traditional secular songs - "Last Christmas," "Snoopy's Christmas," "Winter Wonderland," "Jingle Bell Rock," et. al.
Of the religious songs, probably "Silent Night" and "We Three Kings."
I really don't know a lot of the really obscure or new age stuff. The radio stations around here start right before Thanksgiving and for about 5 weeks play all the conventional songs like I mentioned. Someone named Kimberley Locke has a nice version of "Up on the Housetop." But the Christmas music on the radio is over now. It should run through January 1.
Ideally, American "Christmastime" would run from about December 20th to January 6th rather than starting at Thanksgiving and ending abruptly at around noon on December 25th.
Open presents on the "First Day of Christmas" and then spend the rest of
Christmastide engaging in merrymaking, fellowship and other types of holiday festivities.