I agree that horses are livestock. The definition of livestock is "farm animals regarded as an asset." (Google dictionary) Also "Animals kept or raised for use or pleasure." (Merriam-Webster) The Cambridge Dictionary defines livestock as "Animals kept on a farm." "Livestock" doesn't necessarily mean that the animal has an agricultural purpose. I would argue that all of us consider our horses as an asset in ways that we don't consider our dogs or cats. Horses have economic value, which increases with training and/or show success. That's true of all horses in a way that is not so with all dogs or cats (pedigreed breeding or show dogs/cats do have economic value but the majority of pets don't). As livestock, they are subject to different regulation in some areas, such as where they can be kept, how their waste is disposed of, where it can be disposed of, etc. That makes sense.