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Bitterly cold weather lingered in central and eastern parts of the country on Monday, with some regions experiencing wind chills as low as 25 to 35 degrees below zero.

"Very cold wind chills this morning," the National Weather Service said in an advisory for Wisconsin, warning about the possibility of frost bite and hypothermia if precautions weren't taken.

The combination of frigid air and high winds would produce wind chills of up to 35 degrees below zero from the Dakotas into Minnesota and northern Wisconsin, it predicted.

The Weather Channel noted that Minneapolis saw a 32 degree temperature swing on Sunday, "starting the day at 29 degrees, at midnight, temperatures plummeted to 3 below zero by 10 a.m. And factoring in the winds, it felt closer to 20 below."

Meanwhile, a storm system dumped up to seven inches of snow on parts of New England late Sunday and early Monday.

The new snow brought more winter misery for areas still recovering from a pre-Christmas ice storm that left tens of thousands without power for days.

Efforts continued Sunday to restore power to residents across much of the Midwest and Northeast. Thousands of residents from Michigan to Maine and even into Canada have been without electricity for days, which forced many to ring in the holidays in the safety of a shelter.

Forecasters also warned that the Northeast faces yet more wintry weather in the days ahead.

"It's going to get very interesting in the Northeast in the latter part of the week," said Guy Walton, a meteorologist at The Weather Channel. "Thursday to Friday there is a potential for a very bad storm, what we call a nor'easter. There is potential for heavy snow late in the week for New York City."

NBC News' F. Brinley Bruton contributed to this report.