I know that the environment plays a role in the changing of hair or feathers in some animals so here:
Winter- color changes to more resemble winter surroundings. You'll see more white colors to blend in.
Summer- the colors more resemble the summer colors; you'll see more browns and rocky looking colors to hide/blend in.
Spring- you'll see very vibrant colors like that of a flower.
Those are some examples, but I hope this helps.
