As US schools closed on Thursday to keep children out of icy weather so dangerous it can leave skin frostbitten in 20 minutes, American cities and shelters were working to save the lives of homeless people at risk of freezing to death.

For hundreds of thousands of homeless men, women and children, winter is a matter of life and death. The current cold snap sweeping the midwest and east coast has packed tens of thousands into emergency housing in small towns and major cities alike.

In Boston, where nearly 17,000 people were homeless last year and the wind-chill temperature dipped below 0F (-18C) on Thursday, shelters were at full capacity. At the Pine Street Inn, the largest homeless services agency in New England, around 750 people stayed overnight on Wednesday, spokesperson Barbara Trevisan said. In December the shelter had 16% more men and 24% more women than the same time the previous year.

Trevisan said numbers were up due to the weather and the closure of a nearby homeless center, which has scattered homeless people around Boston. Pine Street transported 100 people to other buildings on Wednesday night when it ran out of room; it sends two vans around the city day and night to try to get homeless people inside.

Lieutenant Mike Harper, an executive director of the Salvation Army Cambridge Shelter for Men, said his refuge also ran out of beds on Wednesday night. “We used all our overflow cots,” he said. “We had people sitting, heads on the tables, just to stay warm here.”

‘When it’s cold like this we won’t turn anyone away’

Every shelter representative who spoke with the Guardian offered a variation of the same sentiment: “When it’s cold like this we won’t turn anyone away.”

Harper said it was too early to tell whether this winter would compare to last year, when his shelter fed and housed 350 overflow stays in January and February. “It puts a strain on the budget but you’ve got to do the right thing,” he said.

Boston’s Public Health Commission has scrambled to restore emergency housing for homeless people since the city’s Long Island Shelter was shut down, due to a condemned bridge, in October. Spokesperson McKenzie Ridings said the city had two new facilities, had opened “warming centers” for the homeless and families with burst pipes, and was handing out blankets and other items to people who refuse shelter. She also said the city would grant temporary amnesty to homeless people who had been previously barred from facilities for non-violent offenses.

There are as many as 138,575 homeless people in Chicago – where the highest temperature on Thursday was forecast to be about 13F (-11C) – according to an estimate by the city’s Coalition for the Homeless. Stephen Welch, executive assistant to the president of the Pacific Garden Mission, said between 1,100 and 1,200 people slept at the “overburdened” shelter on Wednesday night, on beds, cots and foam mats.

“I think we’re probably the only place in the world that has triple bunk beds,” he said.

Families and the homeless have surged to the mission from the cold, Welch said, comparing the recent numbers to an average of 600 hosted during summers. Welch said increasing numbers of young people came through the shelter doors.

“I would say that crack and heroin is bringing a younger group in who are being thrown out of the house,” he said, though he added that many others have come simply due to poverty.

“Three teenagers came in here last week when it was seven degrees and a wind chill of negative 11. I think they’re 17, two boys and a girl, and they were running around the streets without coats. A Catholic charity dropped them off from the hospital and I asked them how they got there. They said they were picked up because the boy’s feet froze in his shoes.”

Crowded quarters mean tempers flare

Both Trevisan and Harper cited mental illness as the main reason some homeless people refuse to come to shelters; Pine Street has coordinated with clinicians to try to convince some to stay. For others “it’s deep trust issues”, Harper said. “They figure they’re safer out there than in the shelters.”

Drugs and alcohol are another problem that shelters face when trying to convince people to stay and to maintain peace inside. Harper runs a dry shelter, which provides a security that he says “a lot of folks appreciate”. He directs visibly intoxicated people elsewhere for the night. Pine Street and the Pacific Garden Mission do not allow intoxicants on the premises but do accept people under the influence, which leads to tensions.

Welch said the Chicago mission has a trained security team that keeps the peace, but the sheer number of people in close quarters sill means tempers flare: “You could have 1,000 Boy Scouts in the building and a fight would break out.” Trevisan said that rules alone – meal times, showers and the like – warded people away from the shelter system. “It’s close quarters, we have hundreds of people here at any given time, and clearly that doesn’t have a lot of appeal to some people.”

Each of the shelter representatives said they coordinated with city police and emergency medical personnel when they encountered a person at dire risk. Boston and New York have “right to shelter” laws that require the cities provide housing, but no city can compel a person to take shelter, so officials and housing workers can only offer supplies to the homeless who refuse to come in. Those supplies often come entirely from donations, as in the case of the Chicago mission.

New York has some 60,000 homeless people in and out of shelters, according to its chapter of the Coalition for the Homeless. The city’s Department of Homeless services enacts a “Code Blue” procedure for severe cold. During a Code Blue, the city relaxes the usual intake process for people who want to access shelters and “drop-in” centers and doubles the number of teams that search for homeless people at risk. In 2014, the city’s annual survey found 3,357 homeless people on the streets and subways.

In 2013 homelessness in the US reached its highest levels since the Great Depression, according to a federal Housing Department report that said 610,042 people experienced homelessness that year. More than a third were in unsheltered locations.