The National Weather Service had issued a lake effect snow warning for Chautauqua and Cattaraugus counties, which remained in effect until 4 a.m. Thursday.
Accumulations between 7 to 12 inches were expected, along with winds of 15 to 30 mph - producing blowing and drifting snow.
More than 2 feet of snow has fallen in central New York areas east of Lake Ontario, while towns south of Buffalo are getting their share of lake-effect snow, the Associated Press reports.
The National Weather Service says the storms that began Tuesday have dumped 24 to 28 inches of snow on towns in northern Oswego County, on Lake Ontario's eastern end, according to the AP. It says 10 to 18 inches are reported in areas of Erie and Cattaraugus counties south of Buffalo.