I can't speak for others but my horses are most definitely not pets. They are livestock.
They don't come in the house, sit in a chair with me, or sleep on my bed. They are in the pasture waiting on my pleasure, whether that be to breed a mare to the stallion, or the mare is carrying a foal to deliver in spring or waiting for me to saddle up and go for a ride or to a show or to help someone with their livestock.
My horses are very well cared for, they have a barn, fresh, clean water 24/7, free choice grass and or hay 24/7, and they are fed a good, healthy diet, kept up on their vaccines, deworming and farrier work. They are groomed and petted and trained, but they exist for my entertainment and/or use.
Don't make the mistake of thinking I don't love my horses, I do, very much. But they are not pets who are not expected to do anything to earn their keep.
My dogs are pets, they are fed, allowed in the house, on the bed, on the couch, the chairs, whatever. They do nothing to justify their existence and they truly are my pets.
My barn cats, while cared for and loved and petted and well fed, are not pets. They are expected to keep this place rodent and pest free for their keep. If one disappears, I miss him but I do not mourn his loss as I would my dogs.
I love my chickens, but they are not pets. Their job is to lay eggs. When they stop laying, their job is to become dinner. My life would be missing something vital if I no longer raised chickens and could no longer laugh at their antics, but they too are livestock.
Just because most people in this country do not "work" their horses as automobiles or plows doesn't make them strictly pets. They are expected to provide entertainment of some sort to justify their existence. Just because we do not chose to eat them when they're too old to work or entertain in some fashion doesn't make them pets.