Monday is a good news and bad news situation.
An arctic air mass entrenched over central North Carolina is to blame for the cold, the weather service said in a statement.
"It's too far out to speculate on how much accumulation we could have", said Corey Mead, meteorologist with the National Weather Service.
A wind chill advisory is in effect for western Dutchess County and a wind chill warning is in effect for eastern Dutchess until 7 a.m. Sunday.
The actual temperature is only expected to reach 10 on Thursday, and Friday's high is forecast to be lower still at 8, with sunny skies both days.
Forecasters say the wind chill will make it feel as cold as zero to 10 degrees below zero Thursday night, and 5 to 15 below zero Friday night into Saturday morning. A wintery mix of freezing rain and snow is forecast for Saturday.
That can result in snow blowing onto roads that have already been cleared, and it also poses the risk of fallen tree branches knocking out power, the weather service said.
Precipitation is expected to move into the area Sunday morning in the form of freezing drizzle and light freezing rain, according to the National Weather Service.
The precipitation was 0.4 inches of snow, pushing the January snowfall total up to 0.5 inches in the capital city.