hepcats (linked with "hipsters" in jazz, especially swing jazz), Keith Richards (for one) talks about musicians as "cats" all the time, the references constantly abound in the lyrics themselves, e.g. The Beatles cover of the Leiber/Stoller song "Three Cool Cats".
Perhaps I am clouded by my liking for cats, but there doesn't seem to be such a depth of reference in relation to other animals in music. Who Let the Dogs Out, anyone?? Yeuchh.
Possibly the only other rival could be birds. Again referrring to jazz, Charlie Parker was known as "Bird", and the bird is frequently referred to in lyrics as a shorthand for some sort of personal freedom. Apart from the aforementioned, though, rarely are musicians referred to as creatures of the winged feathered variety.
Is it because in some way, cats are associated with the unconscious, the rejection of "ordered" living, and a move towards the instinctive? And do musicians therefore tend to like cats more than dogs? It seems that way to me.