I think you have your heart in the right place. I don't know that you have the finances and knowledge to care for these horses. You have basically, 3 horses (probably a gelding/mares as stallions would probably not be co-existing well) that are around ages 15 to 25. You have an older neighbor who is caring for these horses as the owner is MIA. The horses sound a little neglected ie. Hoof care, and feeding are somewhat spotty. If I was in your position, I would contact the SPCA, animal control or try to find an equine rescue. Legally if someone going down the road sees theses horses they could file animal abuse charges. These charges would be leveled against the older gentleman. The owner of the property is often seen as the person responsible for the animal's care. Right now, you don't know for sure who owns the horses. Which to a person investigating an animal abuse/neglect case sounds like a lie.
Having the neighbor pay their expenses is a nice gesture; however, he is entering a retirement home and will not be able to do that for long. The future property owners are not going to let you keep the horses on the property without paying board. If they let you keep the horses on the property at all. Then if you are bound and determined to keep and care for this horse what happens in the winter (when its cold) or in a few years when you (hopefully) go off to college? What happens if the horse gets sick? What happens if it dies? Do you have clearance from current or future owners to bury it on their property? If not can you afford the 500+ dollars that is burial for a horse. In addition, to what could easily be a 500+ dollar vet bill. I know the idea of helping these horses is appealing. I know that the idea of you riding this horse is appealing. I am not sure that you are the right home for these horses or are not breaking the law caring for them. If you are interested in horses I would suggest talking to a rescue/SPCA and then taking lessons yourself at a barn. That way you could learn about horses in a better environment. These horses would be receiving the care they require, which may be both expensive and time consuming.