If the rider is in a public place (at least in Ireland, I can't speak for laws in other countries), then they can expect to be photographed. If the owner/rider complains, then it's good manners to take the photo down, but they have no legal standing and if the photographer refused, there's nothing the rider can do. The only way this would really change is if you hid in a tree and took it, or used the photo to spread misinformation. Unless the subject of the photograph is a minor. The photographer retains copyright of the photo, even if the subject buys the photo, unless they buy the copyright too.
Private property is subject to the owner/occupants.
Scott is right, I would add that you have to be careful on who is the photographer ! If it's a professional for example, he might no want you to share his work without paying for it or without his copyright.