So I was watching TV on December 25th, and someone said, "Wishing all of you out there happy holidays!"
No. That is wrong. It's Christmas. You say "Merry Christmas" on Christmas.
That's like if on Columbus Day, someone said, "I hope everyone is enjoying the Explorer season!" Sorry, Vespucci, today is Columbus Day, you say "Happy Columbus Day." And on Christmas you say "Merry Christmas." The End.