As the temperatures in NYC rapidly declines, the cliche is that there is less for visitors to see and do. As a guide (and a lifelong New Yorker!), I will offer a rebuttal. Visiting NYC in the winter months simply provides different opportunities.
Besides the many indoor activities NYC has to offer-- nearly 100 museums alone-- there are plenty of things outdoors worth putting on the extra layers. Many New York parks are worth exploring in the winter... seeing the lakes of Central Park covered in ice, and its rolling hills covered in snow, are a beautiful sight. Go to the Central Park Zoo and see the red panda, snow leopards, and polar bears in their preferred weather. The New York Botanical Garden's holiday train show (which runs through mid-January) is worth the trip up to the Bronx. Enjoy an afternoon of ice skating at any of NYC's numerous outdoor rinks... Wollman Rink, Rockefeller Center, Bryant Park. And much more.
And if you are planning to come to New York between Thanksgiving and New Years, the city is and endless trove of holiday activities: holiday markets, the window displays along 5th Avenue, the Rockettes, SantaLand at Macy's, and much more.
If you are considering coming to New York in the winter months, take the plunge (like the Polar Beach diving into Coney Island's waters on New Year's Day). New York is the city that doesn't sleep. And it doesn't hibernate either.