A mount is another form of referring to a horse or any animal that one can ride on. It comes from the act of 'mounting', the act of getting up on the animal and riding it.
In this case, Don Quixote's horse is being described as <em>"old and bony, but it was a mount, nonetheless."</em> This means that even though the horse was old and skinny, it can still be mounted. Thus, the mount in the sentence refers to a horse.
