The mice and hare we are familiar with are mammals so cannot live underwater. Mice can swim quite well, but are much happier on dry land.
There are a type of mice and hare that are aquatic creatures, however, but these are not the sort of animals you come across everyday. The sea hare is a type of work that is segmented. This means that its body is separated into definite segments, a body feature typical of annelid worms. In the sea hare, each segment has a small, paddle-like appendage with strong bristles on it that helps the worm burrow into sand.
The marine polychaete Aphrodite aculeata is often called the sea mouse because it has a furry coating of densely matted long fine bristles that cover the surface of its body. The longer bristles on the outer side of the body are reflective and the sea mouse turns all different colours of the rainbow when they catch the light.