What is a grouse Northern Hemisphere with plumage that brown or gray in summer and winter?

The correct answer is ptarmigan.

Ptarmigan are a group of grouse species found in the Northern Hemisphere. They are known for their plumage which changes color from brown or gray in the summer to white in the winter, providing them with camouflage in different seasons. Ptarmigan are typically found in tundra, moorland, and alpine habitats.