My horse was a race horse when I bought her. So we are both registered with Standardbred Canada. She has a tattoo on her neck to identify her, but she's also quite different looking than most horses! I have a lot of pictures of her from all angles too to show all her markings.
I have a bill of sale, import papers, registration papers in our name and what most people use here is called a "Carnet de Vaccin" which is just a historial vaccination card. (Annual vaccines are mandatory) Evidently if you are in possession of that and the horse it is good.
Just a note on this thread, we don't have much horse theft here but in my barn we still take precautions. For instance, we don't decorate our boxes nor do we post information that would indicate a horses value or lineage. The only information on the box door is horses nickname, owners name and contact info, emergency info, medical info, farrier and vet info and feeding/turnout instructions. I also keep a file in the house on each horse that is handy which includes owners info and detailed photos. In case a horse were to ever go missing it is readily available to access and distribute the information. I also photograph and note brands and serial numbers of saddles and expensive tack too.
Luckily, knock on wood, we have never had a problem.
All my minis are registered and the registry now requires 4 photos of each horse registered every time that registry paperwork is done. I also have photos that could fill a small office to the ceiling of my horses around my house, in my barn, around my barn, at shows, both with and without me in them. If someone steals my horse, they will have to be close to my house to get them and most likely would wake me up in the process. I also have the original bill of sale on all but one of them, as he was a trade and I am good friends with the lady and I do not think she would ever try to say he is not mine.