You can't just go around saying that to people! Think of all the religions who have New Year at a different time. And then there's the billion or so Chinese people who celebrate it sometime in Februaury.
No, it isn't P.C. to say "Happy New Year" to people on New Years Day.
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Stupid political correctness. WTF is wrong with saying "brainstorm" for heavens sake?!
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Btw, this year I had not one person say "Happy Holidays" to me. It was all "Merry Christmas!". I think that "Happy Holidays" must be a purely American thing.