There are several winter holidays besides Christmas. Saying "Happy Holidays" is the much more considerate greeting when you're dealing with people that may not celebrate Christmas.Funny that the weeks leading up to Christmas, the atheists were "Happy Holidays" thus and that.
They even defended themselves, saying that Christmas and New Years are the holidays.
Now it's New Year's Eve and the "Happy Holidays" greetings are gone...
We're pretty much all on the same calender around here, so generalizing for the New Year is pointless.