Snow maps, the Thursday storm, Arctic blast, and then we watch the Feb 1st/2nd storm:
Here are the latest snow maps through 7 PM Wednesday from the Euro, Euro ensemble mean, GFS, and RGEM. It looks like mixing with sleet and rain at times will keep accumulations down on Long Island, especially the south shore.
The 5th image shows the Thursday storm staying well south of Long Island and New England and heading due east.
A lobe of the polar vortex will be swinging through the northeast later this week bringing frigid conditions (see 6th image for projected wind chill temperatures at 7 AM Saturday) from Thursday night to early Sunday morning.
Then we will be watching the next storm for NEXT Monday/Tuesday (Feb 1st/2nd) that will be moving into the retreating cold air, so it could be snow to rain for Long Island, but there could be a good amount of snow in parts of New England (see 7th and 8th images for the real early look from the Euro).