In a dilapidated farm shed in New York’s rural North Country, the belongings of a migrant family who quietly took shelter one night were still visible months later: some clothing and children’s shoes, stiffened by the cold and a thin blanket of snow.

Thomas Brassard recalled his surprise when he saw the family — a husband, wife and two children — emerge from the shed as he started his truck in the early morning.

They asked him in broken English if he could give them a ride to the nearest city. He apologetically told them he couldn’t help and then placed a call to the Border Patrol, which quickly detained them.

It has become a familiar scene here in Champlain, N.Y., nestled on the state’s border with Canada, so much so that the mayor keeps knit hats and gloves in the trunk of her car to hand out to the migrants she encounters.

“The weather is so severe you just can’t survive,” said Janet McFetridge, the village’s mayor. “Border Patrol is working extremely hard to save people’s lives because that’s what it’s come down to.”