If your house is painted the same dull brown color as a mouse's fur, you can call it mousy. If you're tired of your mousy hair, you can always dye it purple.
If you think of mice as shy and boring, you'll understand the sense of the adjective mousy. Whether it's describing a color, like your mousy brown sweater, or a personality, like a timid, mousy classmate, mousy is rarely a compliment. The "quiet and unassertive" meaning is the oldest, dating from about 1812, while the reference to color came along forty years later.