This hardy city, more or less unfazed by Sunday’s sub-zero temperatures, is taking no chances with the kind of weather forecast for Monday, when the low is predicted to be minus-24 and the wind chill could drop to minus-50.

Gov. Mark Dayton (D) has ordered schools closed statewide; one big employer, 3M, has told employees to stay home; and Minneapolis has shut down its parks to keep people indoors.

“This is the first time we have used the ‘particularly dangerous situation’ (PDS) wording with a Wind Chill Warning,” the National Weather Service in the Twin Cities tweeted Sunday. Wind chills farther north could approach minus-65, forecasters said, warning that exposed flesh would freeze in minutes.

A large swath of the nation is in the grip of a mass of frigid air that originated in the north, know as a polar vortex, that will bring some of the lowest temperatures in decades, said Jason Samenow, chief meteorologist for the Capital Weather Gang.

Samenow reported on the Capital Weather Gang blog that about 115 million people were under a wind chill warning, watch or advisory Sunday and that the National Weather Service is forecasting that by Tuesday morning, about 1.5 million square miles — or half of the lower 48 states — are forecast to have wind chills below zero, including Little Rock, Atlanta, Richmond and the District. In the east, according to Samenow, Tuesday’s low temperatures will be up to 40 degrees below normal.

Frigid temperatures and strong winds batter the Midwest and Northeast as arctic chill sets in after major snow storm. (Reuters)

Temperatures were predicted to drop to minus-15 at Chicago’s O’Hare International Airport by dawn Monday, prompting major universities and hundreds of schools, businesses and day-care centers to announce they would shut down.

At O’Hare Airport, 1,200 flights — about half the total traffic — were canceled as of late Sunday afternoon, according to the flight tracker FlightAware. Airports in St. Louis and Indianapolis also saw about half their scheduled departures and landings canceled late Sunday afternoon, the same site showed.

In New York, a plane from Toronto landed at Kennedy International Airport early Sunday and slid into snow as it turned from a runway onto a taxiway. No one was injured, and the airport temporarily suspended operations because of icy runways.

Around the Washington region, activity focused on bracing for the incoming cold, with governments publicizing hypothermia hotline numbers, including the District’s (202-399-7093).

In Fairfax County, where wind chills are expected to drop below zero, school engineers and maintenance workers have been checking on heating units and taking precautions to keep buildings warm.

“The severe cold is just another way of Mother Nature reminding us we’re not in charge,” said Jeff Platenberg, the Fairfax County school system’s assistant superintendent for facilities. “With these historically freezing lows, the best thing we can do is remind parents to make sure children are dressed warmly because they will be standing out at a bus stop.”

As commuters readied for the workweek near Washington, they were urged to make several last-minute checks of their vehicles, including levels of antifreeze in their car radiators.

People share their photos and videos of the Washington, D.C. area on Instagram of the on the January 3, 2014 snowday. (Sandi Moynihan & Natalie Jennings/The Washington Post)

“I’m suggesting [doing so] at a professional service center that knows what to look for because it’s such an expensive repair and so cheap to take care of,” said Lon Anderson, a spokesman for AAA Mid-Atlantic. “It’s not something they’ve got to talk about in Minnesota or Wisconsin, where they’re used to zero.”

Minnesota’s preparations qualified as unusual, although not unprecedented, in a state whose residents famously take winter’s cold and snow in stride. The last time a governor ordered the schools closed across the state was 1997.

“I’ve lived here for six years, and I’ve never heard of the cold closing anything,” said Kim Glynn, a physician who was at the Mall of America in Bloomington with her husband and two children late Sunday morning.

But Sunday was brilliantly crisp and sunny, perfect for hockey on the frozen Lake of the Isles in the city’s Kenwood section, where Nelson Fox, Kyle Granberger and Tony Porter were skating in the early afternoon, when temperatures hovered at about minus-7.

“It’s about the only thing to do in Minnesota in the wintertime,” said Fox, 24, who runs a Web development company with Granberger. A warming trailer at the edge of the lake had been closed, perhaps to discourage the kind of activity the three friends were undertaking.

On a trail around the lake, at least two people dressed in heavy clothing — including ski masks — were jogging, and a lone bicyclist could be seen heading slowly into the distance. A couple of dog walkers trudged across snow.

“You’ve got to embrace where you live. You can’t run away from it,” said Nate Peterson, a social studies teacher at Delano Middle School. “Otherwise, you might as well move to Florida.”

Peterson, his wife, Jen, and their 2-year-old, Leighton, weren’t exactly embracing the cold, but they hadn’t run away, either. They had ventured to the Mall of America, one of the largest shopping centers in the United States, which was filling rapidly Sunday afternoon as the prospect of a day at home Monday loomed.

“Normally on the weekend, we go sledding, play in the snow,” Peterson said in the shadow of the mall’s indoor roller coaster. On Saturday, the family had gone to the zoo, but that will be closed Monday as well, because part of it is outdoors. Monday was looking like a day of indoor knee hockey and arts and crafts.

“People are gutsy. People try to show how tough they are,” Peterson said. “When it’s this . . . cold, to us it’s not worth it.”

“We’ll stay inside. It’ll be a long day,” agreed Jennifer Calnon of Rosemont, who will care for two children while her husband works a 13-hour shift as a pharmacist. “We’ll build some forts and finger paint.”

And there will be no hockey Monday for Fox, although not because of the cold.

“I’m flying to Vegas” Monday, he said. “Family vacation.” From there, he said, he would be heading to Tahiti.

Flaherty reported from Washington. T. Rees Shapiro contributed to this report from Washington.