A brown leather loafer came into view on a patch of ice high up in Norway’s Innlandet Mountains. As soon as local hiker and history buff Reidar Marstein spotted it, he knew it was significant.

Those recoveries capture human activity across thousands of years.

In Norway’s highest mountains, experts are scouring perilous terrain for pieces of the past, long stored in mint condition in ice patches. As temperatures rise across the world, glacial archaeologists ...