So basically, what you are saying is that these people own these horses but don't care for them. They are, I'm assuming, boarded on the property? Have they paid board, was there a boarding contract?
Short answer, no you can't claim them. If they came and decided to pick them up, there is nothing you could legally do to stop them.
If you are so worried about paying all the bills for these horses, then tell the owners that they need to start paying for feed/vet/farrier/etc and if they can't then they need to remove the horses from the property.