I think the Grimm fairy tales and Aesop's fables were there first. It probably goes back much farther than that is folklore all over the world.
You're right about mouse animation, though. Mice are non-threatening (excluding the hanta virus) and, when animated, cute--and they sing in those little squeaky voices.
I think the mouse is sort of the Everyman of the animal kingdom. Whether this is an effect of mice being the protagonists in All The Cartoons, or the cause of it, is probably anyone's guess though.
You're right about mouse animation, though. Mice are non-threatening (excluding the hanta virus) and, when animated, cute--and they sing in those little squeaky voices.