At the end of the day, possession is 9/10 of the law.
Many sellers do not realize that a Bill of Sale is a legal document that transfers the title of the horse. Once you hand over a bill of sale to a buyer, it IS their horse, regardless of whether they still owe payments or not. One of the biggest disputes all equine lawyers deal with is over transfer of title or ownership of a horse.
If you have sold a horse on payments, DO NOT combine your purchase agreement and bill of sale all into one. Why? Re-read the paragraph above! Because a bill of sale determines title on a horse, even though a buyer may not have finished paying on a horse, if they have a bill of sale on the horse, THEY OWN THE HORSE and therefore can easily dispute any further payments at a later date! ...which also means, at the end of the day, it DOES NOT matter who's name the registration papers are in. Most Equine Breed Registries will tell you that they are not in the business of proving titles. As many people know, especially in the performance world, a horse can change ownership 5 or 6 times with the registration papers never being transfered. It does not mean the last person listed as owner on the registration papers is the legal or rightful owner.
The only way to combat this HUGE, HUGE problem in our industry, is to realize it is important that a purchase agreement or promissory note be drawn up for buyer that is purchasing a horse through payments, and DO NOT EVER give the buyer a signed bill of sale until all pre-sale conditions have been met. As well, it is important to retain a security interest or collateral interest in the horse, otherwise....you DO NOT have the right to repo the horse. Then your only recourse is to sue for damages! Please note that the States of Florida, California and Kentucky have special requirements regarding bill of sales - which is also why it is so important to not just go on the internet and ask someone for a generic promissory note agreement, etc., as most generic contracts are missing crucial elements. It is sometimes worth it's weight in gold to pay an Equine Lawyer (or a lawyer with a bit of equine knowledge) to draw up your own personal contracts that you can potentially use over and over. If anyone needs a referal to a good Equine Lawyer in their state, email me.
Also note, in your promissory note or purchase agreement, it is so important to make sure a clause is added stating if the buyer does not finishing paying for the horse, you have the right to come onto their property and remove the horse. You DO NOT have a right, as a matter of law, to go on to someone's property and seize or repo a horse unless it is agreed up front.
People have a misconception that a Sheriff or the Police will accompany a seller out to pick up their horse. This is a civil matter. The police are NOT going to help you if you don't have anything in writing or the proper documentation. I know there are lots of shows on TV right now regarding repossession, but it's important to understand that they are not just showing up on someone's property and taking their vehicle just because. They have already gone through the courts and have the proper documentation to back them up.
Hopefully, that answers your questions regarding, "why can't you just go and pick up the horse". Simply put...it just isn't that simple!
If more people would realize stuff like this, as well as always making sure any deals are done by contracts and not just a hand shake and a hope, you would be putting equine lawyers and people like myself (equine appraisers/equine expert witnesses) out of business!