"Did a couple of troopers shepherd/protect Kellerman at a fast walk?"

I doubt it. Rank has its privileges. More likely that someone gave up his horse to the General so the General could ride instead of walk. The grabbing of the bridles would more likely be an emergency maneuver that only had to last for a minute or so to get him out of immediate harm's way if the situation was too dangerous to allow him to take over someone else's horse on the spot.