Since there is only one new year, the plural seems wrong. I think either New Year's Eve or New Year's Day is meant, but the last word omitted for the sake of brevity: What are you doing on New Year's? That may of course be a little inexact, but English often is.
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TakaIs it a typo?It's a feature of American English. Outside that, the s is not included.
AnonymousIt's a feature of American English.My American friends tell me that New Year's may be used for New Year's Eve/Day, but that they say only Happy New Year.