This one has a lot of everything...

Well, here we go again.  This storm has already dumped over a foot of snow and several inches of ice over the heartland and it's going to bring us some snow, freezing rain, ice, and rain.  The problem with this storm is that due to the complexity of the snow/ice line, there is a short gradient between who will receive mostly snow and freezing rain and who will receive more rain.  So for this post, I'm going to address Northeast NJ and Northwest NJ separately.
Let's start with the Northeast.

Northeast NJ will see precipitation move in around 3am in the form of all snow.  By Tuesday morning, some warmer air will filter in to the upper atmosphere.  This warm air will not change us over to rain but rather freezing rain and ice pellets.  The reason being is that the air temperature at the surface will still be below freezing while the air temperature in the upper atmosphere will be above freezing.  This in effect prevents the crystals that usually form snowflakes from forming.  When the precipitation reaches the ground, it is still very cold and will freeze on contact.
There will be a break in the precipitation during the late afternoon early evening hours.  This intermittence will last until the primary storm system moves in from the west.  Around 9-10pm the precipitation will begin again in the form of heavy snow and sleet.  This is where the primary accumulations will take place.  Throughout the overnight hours Tuesday into Wednesday, Northeast NJ will see totals in the 2"-4" range.  Wednesday morning, we will see a quick changeover from snow to sleet and rain.  This will keep totals down compared to the rest of north Jersey.  Total Ice accumulation could be .25"-.40".

Northwest NJ will see a longer period of snow and freezing rain due to the higher elevations and track of the storm.  Northwest NJ will see snow totals in the range of 9"-12" and ice accumulations in excess of a half inch.

As always the exact track of the storm will determine the timing of the changeover and the snow/ice accumulations.  Keep checking in throughout the storm for any updates.