ERIE, Pa. — Shivering, snowbound cities are scrapping their outdoor New Year’s Eve countdowns. Polar-bear plunges are being canceled because of fears of frostbite and hypothermia. Winter-hardened towns are gaping at their new lows: 32 degrees below zero in Watertown, N.Y. Minus 36 in International Falls, Minn.

Record-breaking snowfalls have stranded older and disabled residents inside their homes for days. Cars are buried under mountains of snow, and lethally low temperatures are forcing cities across the Northeast and Midwest to open emergency “warming centers” for homeless residents and people whose furnaces are no match for the cold.

A mass of Arctic air now has much of the north half of the country wrapped in an icy bear hug, and meteorologists expect the single-digit temperatures to stick around for at least another week.

Sign Up for the Morning Briefing Newsletter

“It’s been hell around here,” said Rick Pakela, 73, a retired welder and maintenance worker in Erie whose family was stranded inside their home this week as the city was buried under five feet of snow.

© Kamil Krzaczynski/Getty Images The Chicago River this week. Two cold-related deaths were reported in the Chicago area, where temperatures are expected to drop into the single digits this weekend. As the pileup progressed, Mr. Pakela said his pregnant granddaughter began having trouble breathing and started vomiting. Mr. Pakela said his own truck had been blocked in their driveway, and health problems prevented him and his wife from leaving the house. The family called 911 and waited as firefighters dug a path to their door so they could take his granddaughter to the hospital.

“We were all a nervous wreck,” Mr. Pakela said.

Their neighbor, Mary Foley, 72, spent three days behind a wall of snow that came halfway to the top of her front door. A 12-year-old who lives down the street trudged through the drift to bring her a plate of ham, green beans and mashed potatoes as a Christmas dinner, and Ms. Foley, who lives alone, said she had stretched the food out over three days, not knowing when she would be able to get out.

On Thursday, she was one of about 60 Erie residents waiting for volunteer crews to arrive and dig her out.

“I can’t go to the grocery store or to church or anything,” she said. “I just stay in the house. That’s all I can do.”

Law-enforcement officials said the weather was a factor in several deaths across the country, including two cold-related deaths in the Chicago area and a rollover car crash that killed four people in Kansas. The plunging temperatures prompted cities to urge homeless residents to seek shelters.

In city after city, the heaps of snow and relentless cold bedeviled government services. The deep freeze made it harder to melt icy streets with rock salt, public-works officials said. In Western New York and Pennsylvania, snowplow drivers trying to clear the streets faced an obstacle course of immobilized cars. Cities warned drivers to dig them out and move them, or said they would be towed.

Waterways turned just as treacherous as roadways. In Northern Michigan, two freighters got stranded in the icy St. Marys River and had to be freed by American and Canadian Coast Guard ships…..more here