Here is Arizona, brands have to be applied for and registered with the AZ Agrigulture/Livestock Department.
The brands have to be renewed by the 'owner' every so often (used to be every 10 years but I believe it is more often than that now) We had a brand registered in our name. ONLY the livestock owned by that person is allowed to use it.
The brand comes assigned to where you are allowed to put it, along with the earmarks used on the cattle. Our horse brand was on the left shoulder, the cattle over the right ribs. I have seen brands on jaws, hips, etc....
You will sometimes see cattle here with three or four brands, that were sold, etc.. and rebranded at the new ranch. You are not allowed to run unbranded cattle here. They become 'mavericks' and property of the state!!
Cattle have tough skin, horses are much different to brand as their skin is thinner. If the iron slips on the hair, or the horse moves, it can cause a splotched brand that is disfiguring and hard to read. Many horse owners out west went to freeze branding horses, as it was a neater cleaner brand and not nearly so stressful on the animal.
I would not hesitate to buy a horse with a brand- providing the brand is porportionate to the animal and not disfiguring, if I was going to show it.