(CNN) -- If you thought the snow was bad, just wait for the cold and ice.
"Don't put your tongue on a flagpole today," Connecticut Gov. Dannel Malloy said Friday, advice that may prove useful over the long term.
"We're going to see a warm-up, and then we're going to see another cold snap," he said. "This may be something that we're dealing with for the next 60 days or so."
The National Weather Service offered similar, if less folksy, admonitions: "Very cold temperatures and dangerous wind chills are moving in behind the system," the service said Friday. "Some of the coldest air of the year should arrive by the weekend over the northern tier of the country."
That may mean lows in the -20s Fahrenheit across North Dakota and Minnesota, with wind chills approaching -50, it said.
In Minnesota, which could see its lowest temperatures in a decade, Gov. Mark Dayton canceled Monday's classes in public schools across the state.
The combination of cold and gusts exceeding 30 mph was expected to lower wind chill temperatures to near zero in the nation's capital and to 45 below in northern Maine.
And another storm is forming that will bring blizzard conditions to North Dakota and parts of South Dakota and Minnesota on Friday night and Saturday, the weather service said.
Though temperatures may rise temporarily in the Midwest and Northeast, they are expected to reverse course Sunday and Monday.
In the Windy City, the arctic blast could be the coldest in 18 years, with subzero temperatures from Sunday evening until Wednesday.
The arctic air will dive southward Monday and Tuesday, carrying zero-degree cold as far south as Nashville.
In the Northeast, the heavy snow that upended routines for about a third of the nation's residents on Friday had tapered off by noon, but snow drifts were complicating the cleanup, in some cases requiring replowing of streets that had already been cleaned.
New York was draped Friday in a near-10-inch layer of white, but that didn't faze some residents.
"A lot of people are walking, and some were even running in Central Park," said CNN iReporter Matthew Burke, who snapped a photograph of the entrance to the park at Fifth Avenue and 72nd Street.
"It's freezing," he said. "I had three layers on, and I was still cold."
It was not expected to get better. Temperatures in Central Park were predicted to drop to zero Friday night for the first time since January 1994.
The snowfall abated early Friday in the nation's capital and was expected to stop in the afternoon in Boston, which got nearly 15 inches.
North of Boston, residents of Topsfield were inundated with nearly 2 feet of snow.
Weather knocks out flights
Across the country, the weather wreaked havoc on airlines' flight schedules.
FlightAware.com, which tracks cancellations due to weather and mechanical problems, said that more than 2,200 flights had been canceled for Friday within, into or out of the United States. That's after more than 2,600 U.S. flights were canceled Thursday.
Flights resumed by late Friday morning in much of New England, though delays were common, and ticket holders were urged to check with their airlines.
Barb Plooster had planned to fly Friday from Erie, Pennsylvania, to Grand Rapids, Michigan, but her flight was canceled. She told CNN affiliate WICU that she was on the phone with United Airlines for five hours trying to find a way to get home but has concluded that she will have to wait until Monday. "We got a warm place to stay, get to visit the kids, the grandkids, so it's OK," she said.
Here's a breakdown of what to expect where:
New York and Long Island
In New York City, Friday's high was predicted to be 18 degrees, and the temperature was expected to go below zero by nightfall, Mayor Bill de Blasio said.
He urged anyone who might see a homeless person to call 311, "and an outreach team will go out immediately to help that individual."
But the newly sworn-in mayor -- who shoveled in front of his home in Brooklyn on Friday morning before handing off the duty to his 16-year-old son, Dante -- praised his team for their work.
"I'd give everyone an A" for effort and effectiveness, he said, but noted that their work was not over.
"Ask again in a few hours," he said. "This is an hour-to-hour thing."
New York had gotten nearly 10 inches of snow by the time it abated late Friday morning, de Blasio said.
Sanitation workers were on 12-hour shifts to clear the city's 6,200 miles of roadways, he said.
Flight operations resumed late Friday morning at John F. Kennedy International Airport; they were continuing -- despite hundreds of cancellations -- at LaGuardia Airport and Newark Liberty International Airport.
Single-digit temperatures were predicted for Saturday morning.
New York City public schools were closed Friday.
The weather had its fans. In Rochester, New York, CNN iReporter Blake Sampson, 29, took a picture from his apartment window. "I grew up in Minnesota, so I'm used to it," he said.
"I like how quiet things get when there is a fresh blanket of snow."
That blanket covered Boston, which expected to see 10 to 18 inches of snow and temperatures as low as 6 degrees below zero by Friday night.
But limited flights were continuing into and out of Boston's Logan International Airport.
The state's emergency management agency predicted up to 2 feet of snow on parts of the North Shore, South Shore and Cape Cod.
Students in scores of school districts were told to stay home Friday.
"I guess Mother Nature wanted to give me one more gift," Boston Mayor Thomas Menino said Thursday, one of his last days in the office he has held since 1993.
Chicago and points beyond
The cold could affect NFL playoff games this weekend:
Saturday's game between the Kansas City Chiefs and the Indianapolis Colts will be played at around 32 degrees, but those inside the Colts' dome should be a little warmer.
On Saturday night, the New Orleans Saints will play the Philadelphia Eagles in the City of Brotherly Love, where the forecast was for 24 degrees and clear skies at kickoff.
In Wisconsin, the Green Bay Packers will give a cold welcome to the San Francisco 49ers on Sunday, when wind chills could be -30.
"This is not the norm," Packers head coach Mike McCarthy told reporters Friday. "It's obviously challenging mentally and physically, and this will definitely be the case Sunday."
When the San Diego Chargers face off Sunday afternoon against the Cincinnati Bengals, a snow storm may be moving through the area.
The U.S. weather has had international implications, too: All meetings were canceled Friday at the United Nations headquarters complex on New York's East Side.
CNN meteorologists Dave Hennen and Sherri Pugh and CNN's Lateef Mungin, Jareen Imam, Kristin Hamill, Chuck Johnston, Ashley Fantz, Greg Botelho and AnneClaire Stapleton contributed to this report.
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