There's been a major brouhaha the last few years over the phrase "Happy Holidays." Some people consider the phrase fightin' words, claiming people should say "Merry Christmas." On the other hand, you may have seen the meme that notes how the world's seven major religions celebrate 29 different holidays between November 1st and January 15th, so it only makes sense to wish people "Happy Holidays," especially if you don't know which one(s) they celebrate. And at the very least, there's Christmas and New Year's, which is two holidays, so "Happy Holidays" is mathematically accurate.
Another phrase you sometimes see this time of year is "Season's Greetings." I say "see" because practically nobody is going to spot a friend at the mall and say, "Hey, Fred, season's greetings!" It's more commonly found in print.
Fifty years ago, during the 1966 holiday season, CBS-TV put the phrase into an animated holiday greeting by R. O. Blechman, whose work, including many magazine covers and ads, has been honored with a retrospective at the Museum of Modern Art. The 60-second film was broadcast during the holiday season for many years thereafter. If you are old enough, you will probably remember seeing it. If you aren't, watch it here. It's quiet and lovely and well worth a minute of your time.