The new bout of snow could bring three feet (1 meter) of snow in parts of Erie County, which includes the city of Buffalo.
"That's a year's worth of snow," said Deputy Erie County Executive Richard Tobe, noting a state of emergency remained in effect.
Driving was banned on many roads and 140 miles (225 km) of the New York State Thruway along Lake Erie and Lake Ontario were closed.
The storm inundated some areas, with snow falling at a rate of 5 inches (13 cm) per hour, while sprinkling only a few inches (cm) just a few miles (km) away, said National Weather Service meteorologist David Thomas.
The disparity is typical of the so-called lake effect, which occurs when cold air moves across the relatively warm Great Lakes, drawing in moisture and dropping snowfall onshore, Thomas said. The phenomenon can create intense squalls but leave nearby locations virtually unscathed.
In south Buffalo, snowmobiles were being used to respond to emergency medical calls and rescue stranded motorists while some 5,000 tons of snow was removed from the area, Buffalo Mayor Byron Brown said at a news conference.
New York Governor Andrew Cuomo declared a state of emergency for 10 counties, deploying National Guard troops to help residents.