I'm not 100% certain where Farriers rode in battle. I believe, like their infantry counterparts, Farriers were attached to the HQ and rode with the color guard; but, that would have varied army-to-army.
It may also have varied between heavy, medium and light cavalry regiments. With the heavy cavalry the whole regiment tended to move as a single block; while a light cavalry regiment could have squadrons detached and fanned-out over a wide area. In one case, much of the HQ would maneuver with the whole; in the other case, the HQ would remain stationary while scouts and skirmishers radiated outwards from that hub.
Again, some armies followed commonsense policies and other armies followed bizarre traditions without any respect for rhyme or reason. So, what may have been a universal practice in the French Imperial Guard might have been considered intolerable nonsense in a British regiment of horse.