On the march or on campaign it was usually only the Battalion Commander who was mounted. All other officers, from subalterns to majors, marched and fought on foot alongside their men.
In addition, any of these more junior officers who chose to be mounted provided an obvious target for enemy sharpshooters.
This particular Battalion Commander would probably be at the rear of his men at the centre of his battalion able to better view the situation from his horse's back and issue orders accordingly.