For all of northern New Jersey snow should begin to fall during the day tomorrow and some places, depending on how far west, and elevation will play a key role. Eventually everyone will go over to sleet/freezing rain and most of us will end as some plain rain, but not all.
The models show warmer air coming into the picture but right now outside my house its 16 and it seems unlikely that all this cold air is going to leave anytime soon. Cold air will dam up against the Appalachian mountains and provided a nasty ice storm for parts of Warren, Sussex, Morris, and western Passaic, in fact schools closing on Wednesday could be a possibilty in those areas. Areas farther east toward Kean university for example will warm up much faster and accumulations will be little if any. Here is the NAM model on the storm, don't be fooled, the warm air is only aloft.
Here is my first guess at the snow totals, come back tomorrow for an update on the snow totals: