During the 17th-19th centuries, many cavalrymen opted to use ranged weapons and fight on foot during actual battle, while utilizing the speed of horses to move around the battlefield quicker when not in actual combat. These regiments were often known as dragoons. What I would like to know is, when these regiments took casualties while dismounted and fighting, what did they do with the horses that no longer had riders? Did they just let them go running off into the wild, or did they try to manage the logistical hassle of taking them with them?
Depends on who supplied the horses, and how critical the needs of the regiment were, if it was the individual who supplied the horse it would go back with the individual if he we wounded or would go back to next of kin, most likely it was written off as killed as well and issued to surviving members who needed a horse if theirs were no more, if if it was government issue which was the case later on it was reissued to the regiment or kept in reserve