Updated NWS snow map and detailed discussion as they decided against a Blizzard Warning:
Here is the newly updated snow map from the National Weather Service. The 2nd image is the current radar at 4:24 PM. The 2rd to 5th images show the simulated future radar for 8 PM, 11 PM, and 1 AM from the HRRR model.
Here is the detailed discussion from the NWS covering Long Island and the tri-state area:
Snow has started over portions of northeast New Jersey, New York City, and Long Island and will continue to overspread the area from southwest to northeast over the next several hours before rapidly increasing in intensity around 7-8pm. Moderate to heavy snow is then expected across the entire region through midnight. While snow will continue inland, things get tricky after midnight along the coast. The 12Z NAM continues to indicate a 2-3C warm nose developing between 700-800mb across Long Island and perhaps portions of coastal Connecticut for several hours overnight. With temperatures generally remaining below freezing at the surface, this would allow for a transition to sleet or a mix of sleet and snow. The south fork of Long Island could even see a transition to plain rain as surface temperatures rise a few degrees above freezing. In addition, high resolution models are indicating the potential for a dry slot to develop across Long Island and perhaps as far north as southern Connecticut. Model soundings also indicate some loss of saturation in the dendritic growth zone during this same period, all of which could at the very least limit the intensity of precipitation, and possibly allow precipitation to change to drizzle for a period. With that said, global model soundings remain below freezing throughout the event, keeping precipitation all snow. Winds will become more northerly as the low pulls east towards daybreak, which will allow colder air to filter back into the region, changing precipitation back to snow everywhere. Snow will eventually wrap up from west to east from late morning into the early afternoon. Snowfall accumulations will range from 12-18 inches across the Lower Hudson Valley, interior northeast New Jersey, and interior southwestern Connecticut, where precipitation will remain all snow. Snow totals will range from 10-15 inches across much of the New York City metro area and western Long Island, although totals could be a few inches lower across coastal portions of Brooklyn, Queens, and Nassau County. Across the rest of Long Island and far southeastern Connecticut, snowfall totals will range from 4-12 inches, lowest across the Twin Forks and immediate south facing coastlines. In addition to the snow, winds will increase this evening as the deepening low approaches. Winds could gust to 35-45 mph across much of the area overnight, with gusts to 45-55 mph possible across far eastern Long Island. While these winds would result in blizzard to near-blizzard conditions at times, they also correspond with the greatest potential for mixing. With that in mind, made no changes to headlines, with a Winter Storm Warning remaining in effect for the entire area. While breezy conditions will continue into the morning as precipitation changes back to snow, with decreasing snowfall intensity visibilities should remain above 1/4 mile.