The building of the ice house signifies that Miyax has decided to reject the ways of the white, "civilized" world, and embrace the old Eskimo ways instead.
The central theme in the book is Miyax's struggle to find her cultural identity. She has experienced the best and worst of her own Eskimo culture; the best being the idyllic time she spent with her father, the great hunter Kapugen, living close to the land in harmony with nature, the worst being forced to become a child bride in a marriage arranged by others. Miyax has also lived for a time in the white world, which sought to distance her from her Eskimo heritage.
When Miyax first set off across the tundra alone, her objective had been to reach Point Hope. She wanted to be in the safety of "civilization"; she was afraid she would perish alone on the frozen land. During the time when she was lost on the tundra, she developed an appreciation for the value of the "old ways", learning the ways of the wolves and recalling what Kapugen had taught her about surviving on the land.
After the great wolf Amaroq is gunned down by the hunters' planes, Miyax's change in attitude becomes definitive. When she thinks of the cities of the white world, she thinks "about the airplane and the fire and blood and the flashes and death". When she thinks of the old ways, she thinks "about peace and Amaroq".
When she builds the ice house, Miyax's choice is clear, at least for that moment. She will "live like and Eskimo - hunt and carve and be with (her wild bird) Tornait" (Part 3).