When I lived and rode in Texas (San Antonio), we had a couple of routes that took us by several Ranches with horses, cows and even a Buffalo. We we told to keeping riding in a normal manner and all would be fine. Several times, the horses would race along the fence with us making for a good work out. Just maintain a normal pace and if you are coming up on a Horse and Rider, politely alert the rider to your presence so they can maintain control over their steed, just in case.
(Howdee Mr. Beanz!)
MM