Tradition and aesthetics.
It's obviously a danger to the animals, but if the police don't give a shit about human life, I'm baffled as to why you think they would care about their dogs and horses. They treasure them as possessions, I'm sure, but if they wanted to keep them out of harm's way, that's what ranches are for.
These are working animals, defined fundamentally by their usefulness to humans. While I cannot speak for other places, this seems consonant with the general American cultural perspective on animals, aside from household pets. They do have certain "rights" under the law, but that doesn't include the right not to be worked to death or put in dangerous situations, just some weak protections against direct physical abuse.
I'm sure the officers who work with the animals would get weepy talking about how much they love the animals, mind. Emotions are a funny thing, as subject to cognitive dissonance as anything else.