We were spectators at Cedar Creek and saw one of the Cavalry horses "bolt," hightailing it back toward the Cavalry camps quite riderless. A minute or so later one of the Cav, troopers made chase and galloped off in the same direction and returned a few minutes later leading the riderless steed back to its rider. I guess it happens.
Your picture is great. It reminds me of an actual occurrence during the original battle at Cedar Creek October 19, 1864. During the fighting up on Red Hill, behind Belle Grove where the 6th Corps had camped, an adjutant of the 9th NY Heavy Artillery was shot from his horse, and it bolted. The horse ended up stopping the battle for a time because it galloped riderless back and forth between the opposing armies as each army tried to call it into their lines. Finally, after about fifteen minutes of this it ended up back beside the adjutant - probably looking exactly like your photo.