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.

“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.