Translated from: http://www.h6.dion.ne.jp/~romandou/015_yukionna.html
The site says the story is taken from Tales of Mystery from Hokkaido「北海道ふしぎふしぎ物語」by Ichido Goda (合田一道) and is titled, “Yuki-onna.” The story takes place when Japan was trying to convince people to settle in Hokkaido so they could stake a stronger claim to the island than the Russians (circa 1869 to 1882); although, admittedly, I’m not very familiar with the history of Hokkaido. In this story, a man from Yamagata is the main character.
On a snowy evening, a young man saw a white woman standing on the bank of the Sorachi River. The young man had left his lover in his hometown in Yamagata to find work in Hokkaido and was lonely. When the woman invited him over to her, he thought that she greatly resembled his lover. He went to see her and slept with her. Her body was as cold as ice, but the man held her tightly as though in a trance. At dawn, when the man awoke, the woman was gone. And his futon (blanket bed) was soaked with ice water.
Every night the man went to see the woman, he held her frigid body and rapidly grew weaker and weaker. His coworkers began to worry about him and one night they followed him. They saw him go to a cave by the river and fall asleep hugging an icicle. (Evidently they do nothing about this???)
Eventually, the man’s frozen corpse was found. People said the woman had been Yuki-onna, but that her true form was the lover he had left in his hometown. When he had left her, she was terribly lonely and became sick and died. Her spirit had come to be with the man she had loved.