Could be snow, but often clear blue skies though very cold. The shops will have their windows dressed for Christmas. The Christmas Tree and the Ice Rink at the Rockefeller Center (ride to the top of the center for marvellous views). Walk across the Brooklyn Bridge. Stroll through Central Park.
Look at the City Breaks and America forums for lots of info. also The Trip Advisor Website has a host of tips and information about New York.

It really depends on how long you will be there with regard what you need to see.

I have been to NY twice, once for Thanksgiving in 04 and Mid January in 06. Both times had great weather and only wore a light jacket. However the last day we were there in 06 there was a light snow fall and the weather changed and boy was it cold. Never new it could get so cold. I was wearing denims and it was so cold my legs were numb so maybe bring a pair of wolly tights or long johns for under your denims.

Woohoo we are also going in December this year. Stopping off for 3 nights enroute to Orlando.