Wonderful idea if you are prepared for the cold.

Christmas in New York City has its own charm.  It won't be as crowded.  The streets and stores look pretty, provided no snowfall in previous days.  You can probably get post-Xmas deals as well.

But,

make sure you are bundled up.  New York is a walking city.  Because of the tunnel effect between the high-rises, the wind can literally freeze you solid.

Happy Holidays!