Hi Maga
In my opinion, December is THE perfect time to go to New York - it'll really get you in the mood for Christmas. We've been a few times just before and just after Christmas, and we loved it. Just be warned that it will be REALLY busy though.
Regarding the weather,
http://www.weatherunderground.com/US/NY/New_York.html is a great site to check what the weather was like on dates in the past. Half way down the page is a section called "History & Almanac" - within here you can type in previous dates and see what the weather was like then. I love the site and could play on it all day if I could!!!!
U2fan