Anyhow let's start off with the basic trend the models are all going with:
Now I know what your thinking. It looks like a horrible setup, and it is. But when systems like this run into the cold air in place we have something called "warm air advection snow". I'm not going to put to sleep by explaining what that is, that's why we have google. Most places will start off as snow but the further south you are the less you get. Let's look at a sounding for Andover Airport in Sussex county.
The line with the blue squares is the freezing line. With the temperature and dew point below freezing with a saturated atmosphere this sounding says it's snowing, and very hard. We have about a 3-5 hour window of snow before a quick change out to sleet and rain occurs. In that time frame the total QPF is between 0.25"-0.50". One issue that will plague the lower elevations is that the surface temperature will be too warm for the snow to accumulate. Areas below 500 feet (south of I-80) will get minimal accumulations. For this reason the total snowfall around High Point, West Milford, and into western Morris will have the highest amounts (simply because surface temperatures will be below freezing).
It's still several days out so this is just a "preliminary" snowfall map. I will be updating when the situation becomes more clear.