MADISON, Wis. — The Upper Midwest remained locked in a deep freeze Wednesday as the bitter temperatures crept eastward where at least one mountain resort warned it was too cold even to ski.

Overnight, ice-covered Chicago firefighters spent hours fighting a massive fire at a warehouse on the city’s South Side, hindered by the single digit chill.

The cold snap arrived Saturday night as waves of Arctic air swept south from Canada, pushing temperatures to dangerous lows and leaving a section of the country well-versed in winter’s pains reeling. The National Weather Service said states from Ohio through to the far northeast of Maine could expect to be slammed by that Arctic blast on Wednesday.

The numbers so far are chilling in themselves: 35 below at Crane Lake, Minn., on Tuesday; Embarrass, Minn., at 36 below on Monday; and Babbitt, Minn., at 29 below on Sunday, according to the National Weather Service.

The weather service issued a wind chill warning for Wednesday in the far north of Maine. In Presque Isle and Caribou, temperatures are not expected to rise above 7 below. And the wind chill could make it feel more like 40 below. Vermont was similarly afflicted, with wind chill advisories and highs peaking in the single digits. Forecasters said Boston and New York City could expect temperatures in the double digits, but that the wind chill would make it feel 5 below. And in mid-Massachusetts, high winds up to 30 mph in Worcester will add to the weather misery.

At least one ski resort in New Hampshire was planning to close Wednesday and Thursday because of the extraordinary cold. Wildcat Mountain in the White Mountains region said it was expecting temperatures in the negative double digits and a wind chill of 48 degrees below zero — conditions that would not be safe for guests or employees on the slopes.

Late Tuesday, some 170 Chicago firefighters — approximately one third of the city’s fire department — turned out in frigid temperatures to battle a blaze at a warehouse on the South Side. Officials said the fire prompted the department’s biggest response in recent years, according to The Chicago Sun-Times said. Despite the scale of the fire, firefighters’ soaked jackets and hats froze, and icicles formed and dangled from hoses and hydrants.

Authorities said exposure has played a role in at least four deaths.

On Sunday, a 70-year-old man was found frozen in his unheated home in Des Plaines, Ill. And in Green Bay, Wis., a 38-year-old man was found dead outside his home Monday morning. Authorities in both cases said the victims died of hypothermia and cold exposure, with alcohol a possible contributing factor.

A 77-year-old Illinois woman also was found dead near her car in southwestern Wisconsin on Saturday night, and a 61-year-old Minnesota man was pronounced dead at a hospital after he was found in a storage building Saturday morning.

The bitter conditions were expected to persist into the weekend in the Midwest through the eastern half of the U.S., said Shawn DeVinny, a National Weather Service meteorologist in suburban Minneapolis.

Ariana Laffey, a 30-year-old homeless woman, kept warm with a blanket, three pairs of pants and six shirts as she sat on a milk crate begging near Chicago’s Willis Tower on Tuesday morning. She said she and her husband spent the night under a bridge, bundled up under a half-dozen blankets.

“We’re just trying to make enough to get a warm room to sleep in tonight,” Laffey said.