In July of 2013, historians shared lots of facts about the Battle of Gettysburg, which was fought fifty years ago, July 1-3 of 1863. A large part of the Confederate Calvary, Stuart's horsemen, never made it to that battle. I cannot say for sure about the presence of an animal that was ridden by a different horseman. In fact, not much has been written about the role played by any horse during those three days.
Still, I have read about the role that one horse played in the Battle of Hanover on June 1, 1963. On that day, General George Custer tied his horse's reins to a tree, one located along a sidewalk in Hanover's center square. Custer's servant made sure that the same animal would be able to aid the start of a quick getaway.
Unlike the forced waits of most horses, this one has been memorialized. The tree on that sidewalk died in 1924, and Hanover's residents wanted to memorialize a plant that had its life cut short by decay. Thus, those residents arranged for the building of a small memorial, one that would explain the tree's place in history. By arranging for construction of that memorial, those Pennsylvanians managed to highlight the patient wait of one four-legged animal, one that was ridden by a rather famous horseman.