Personally, I wouldn't see why not. If you do not have any horses and have horse experience, then it would be a nice oppertunity. If you can work through the problems that they might have and take lessons with a good trainer. I have to warn you though, even if these horses are relatively healthy, old horses are set in their ways. While you can "teach an old dog new tricks", it might prove very difficult. If he is bucky, you will have to train him out of it. Even if you haven't fallen off of him yet, there is no reason that he won't buck you off. Since he is older, I would see if you could get a vet or trainer to go with you to look at him. Make sure they know their stuff, and know if he is healthy enough to do what you want of him.
Keep in mind that he won't be able to jump forever if he can at all. You might have to just settle with a trail horse, which isn't nessisarily a bad thing. I don't see anything strikingly wrong with him. His back is swayed, but it seems just like that of an old horse.