It's a fallacy that reins stop horses. Think about it for a minute. you are 1 sitting on top, so no contact with the ground. 2 you are pulling aginst the sensitive mouth of half a ton of horse 3 This is going to cause said horse discomfort,4 Horse's tend to run away from things that hurt.
The answer, think 'stand still', your body will stop, so will the horse.
I have seen some beautiful model traction engines on the circuit, so is possible to make a steamer.