Here are the maps from the new Euro run as it has the storm farther east and not quite as strong. While there is the potential for some snow mixing in on Long Island, it generally looks like close to 2 inches of rain with gusts of 30 to 45 mph (highest in eastern Suffolk). The rain should end from west to east from mid or late afternoon into early evening on Saturday.
The last image shows the projected snowfall from the National Weather Service, but that will likely be increased later this afternoon.