The National Weather Service warned of "dangerously low" temperatures in some parts, saying people who left their homes were putting their lives at risk.
Snowstorms and heavy winds also badly disrupted travel throughout the region.
Boston Airport was closed on Sunday, forcing the cancellation of hundreds of domestic and international flights.
Some 3,000 flights across Midwest and the north-east have been cancelled over the last two days, leaving thousands of passengers stranded.
School classes cancelled
Massachusetts Governor Mitt Romney declared a state of emergency in his state where up to 39 inches (96cm) of snow was expected.
In addition, meteorologists warned that temperatures could plummet to zero Fahrenheit (-18 Celsius) in some places.
"This is likely to be a record-setting snowstorm in Boston when comparing against data dating back to 1892," National Weather Service forecasters said.
Monday classes were cancelled for many Massachusetts schools, as officials urged non-essential state workers to stay home.
More than 27,000 households were left without power in some parts of the state.
At least 13 deaths have been linked to the weather in Midwest and the north-east.