“Xmas” has been used in English for centuries. The X is an abbreviation for Christ, from the first letter of Greek Christos. First appearing in English in the Anglo Saxon Chronicle in the early twelfth century, it was spelled with Xp or Xr, corresponding to the Greek “Chr,” thus Xres mæsse meant “Christmas.”
Haliday, a thirteenth century term, came from Old English haligdæg, or holy day from halig “holy” and dæg “day.” The meaning “religious festival” came to be equated with something like “day of recreation.” In American English, “the holidays” are exclusively associated with Christmas and the new year. The religious roots are undeniable, so “happy holidays” is as authentic a Christmas greeting as any other.
Note: Colonial American Puritans banned celebrations of Xmas owing to its pagan origins, and because wassailing and caroling by the hoi polloi encouraged rowdy demands for drinks from more prosperous citizens. Thank Anglicans, Catholics, and Lutherans for bringing Christmas celebrations to America. December 25th began festivities that lasted until January 6 (the Twelfth Day, also known as Epiphany) the big day for balls and festivities.