The mistake is thinking that horse , like cars, "steer" by pulling this or pushing that. Yes, there are systems to make a horse move this or that direction. But you aren't actually forceing the horse to go left or right. When you steer your car, you move the wheel to the right and the car goes exactly and porportionatel that direction. It has no choice, it is "forced" into that move (Thank God!).
But steering a horse is differenct because you do not force the horse right or left. You CUE the horse to do those moves on his own. Thus, once the hrose has taken the cue and begins to execute the move, you may no longer be "steering" but just allowing him to finish up the requested manuever.
Since different horses have different willingnesses to accept your cue, and different horses need a stronger cue than others, no two horses will "steer" the same.
The better you get as a rider, the better you become at adapting your cues to fit the horse, and also working with a dull horse to make him more willing to listen up , when lighter cues are given.