Personality is inheritable in general. With my mice, I purposely bred the pairs that didn't bit and would go calm and content when handled, despite no prior handling. I now have mice that once I catch them will happily sit in my hands and clean themselves. I have a buck goat that all his offspring are calm and docile creatures. If you breed two hot tempered horses together, you'll probably get the same with the foal (explains why most horses of a certain breed act similar).
If you breed your animals carefully, there's no reason on why you should get an aggressive animal, with the exception of recessive genetics.