Snowy Night Village is where Yuki-onna lived. A long time ago, a man tried to climb a tree to get a better view of the village. However, the man ended being burned alive and never returned to the village. In a fit of rage, all the men from the village attacked the tree, but they to died.
One of the wiser women from the village realized there was a God living inside the tree. To quell it's anger, the woman sacrificed herself. From her ashes, a baby boy was born. From then on, every year a woman is sacrificed to quell the god and keep the village alive.
Later on, when Asagiri agrees to become the sacrifice, she realizes that the God turned the past sacrifices into the Ghost Hag's, and was merely feeding off of the village. Using the last of her power, she destroyed the God. However, as a result, Snowy Night Village was destroyed, and everyone living in it was as well.
"Snowy Night Village" refers to the fact that the sun never shines in the village, and the village is located on a high mountain.