I'm a little confused... If you are asking about general weather in the greater NJ/NYC area, it will be cold, always a chance of snow. Coming in early would be highly recommended.
If you're asking "when" it will begin to warm up when departing from NJ/NYC it varies but, the first day you board and the first full day at sea are usually "indoor" days but, by the second full day aboard you should be able to get outside.
Also, why not consider joining us for the 2010 Mystery Holiday Cruise out of Bayonne, we have a wonderful group going and the more the merrier!
Hopefully I answered your question and if not, let me know