Dad had a horse drawn dump rake, a little larger than that and used two horses. His was foot operated to raise the teeth to dump the hay; didn't have a lever like that one. It was a very dangerous piece of equipment to operate.
Notice that the operator has nothing to hang onto. If the horse(s) run away, the operator usually fell forward and was dragged and tumbled by the rake teeth, often resulting in death.
Dad had a bucker with a horse on each end to bring the hay up to the hay stacker. He sat on the back as a counterweight to keep the long teeth from catching in the ground. If the team decided to run away with the bucker, all he had to do was let loose of the lines and step off of the back; that allowed the teeth to jam into the ground and stop the team real fast. If the horses were smart, they never tried a runaway when pulling the bucker.
My job when I was 6 years old was to drive the team that pulled the over-shot stacker part up with a bucker load of hay and dump it onto the hay stack, where my two older brothers leveled the stack with pitch forks.
That was the way that we put up hay until Dad bought a hand-threaded wire tie baler about 1948.