Introduction
Skadi is a giantess, daughter of the giant Thjazi, associated with winter, mountains, skiing and hunting. After her father's death at the hands of the gods, she came to Asgard fully armed, demanding compensation, and was given, among other things, a husband chosen under unusual conditions.
This article follows Old Norse mythological tradition, chiefly the Poetic Edda and Snorri Sturluson's Prose Edda, noting where the two sources differ.
Family
Seeking compensation
After the gods killed her father Thjazi (in retaliation for his kidnapping of Idunn), Skadi arrived in Asgard in full armour, ready for war, demanding redress. The gods offered her a settlement: she could choose a husband from among them, but by looking only at their feet, and, separately, the gods agreed to make her laugh, which Loki eventually managed to do through an absurd stunt involving a goat.
Marriage to Njord
Choosing the most beautiful feet, Skadi believed she had selected Baldr, but the feet belonged instead to Njord, and the two were married. The mismatch between her mountain home and his home by the sea proved unworkable: neither could bear the sounds of the other's homeland, and the marriage did not last, with the two living apart.
Later unions
In some later sources, Skadi is said to have subsequently taken up with Odin, or married the god Ullr, reflecting a somewhat fluid tradition regarding her place among the gods after the separation from Njord.
Associations
As a goddess of winter and the mountains, Skadi is sometimes connected to skiing and hunting on snow, and her name has been linked etymologically, though not without debate, to the region name Scandinavia itself.