Since your horse was an Amish buggy horse for several years, he probably has some arthritis in his ankles (fetlocks). The arthritis may not be a problem if he is on soft ground and not having to work much. When he gave the buggy rides, he was likely working on hard ground/road which creates more concussion on joints. Also, when an individual (human or horse) is not in shape, it is easier to sprain/strain something with too much work or working too long.
As for treatment, there are several things that you could do for him. First, make sure that he is turned out to pasture as much as possible. Moving (at his own pace) will help his joints move more freely. It is important for all horses, especially as they get older and have more arthritis, to be able to spend as much time as possible outside. Massaging his legs may also be of benefit and will allow you to follow the progress of the swelling. Finally, if he is still stiff and uncomfortable looking, call your veterinarian. A physical examination and possibly X rays will determine if the cause is truly arthritis and how he should be managed in the future. Also, your veterinarian may prescribe medication that may be beneficial to his joints.