Snowfall was expected to end this morning, but drivers were asked to use caution while driving, the weather service said.
A total of 1 to 3 inches of accumulation is expected between now and when the advisory runs out at 6 a.m. on Monday.
STV weather presenter Sean Batty said: "It is looking likely that higher areas of central, southern and eastern Scotland will see some snow falling by the end of Christmas Day".
Snow, which has been slow to develop this evening, will start overnight - look for it by 10 p.m. - and then evolve into a significant lake effect event that could deliver up to 6 inches of lake effect snow on Christmas Day. But the National Weather Service has emphasized wind could be a larger problem, with possible wind gusts of 40 or 50 miles per hour blowing snow back onto plowed roads. Those high winds may break tree branches and cause scattered power outages. Expect areas of blowing and drifting snow, with wind gusts of 30 to 40 miles per hour, reduced visibility and drifts, which will make travel hard at times.
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A winter weather advisory is in effect to 7 p.m. Monday for Steuben County. South wind around 7 miles per hour will become northeast after midnight.
There is no white Christmas in the United Kingdom again this year as temperatures rose higher than Spain and Turkey. "It's nice to see but it does present hazard". There is a chance of more snow on Thursday and Saturday.
Temperatures will range from the mid teens to low 20s degrees, Fahrenheit, Sunday night, rising into the mid 20s to lower 30s on Christmas Day.