I saw this photo when watching a documentary about wheat. I had to stop and rewind and count the horses. When I saved the photo to my desktop, it was labeled as a 26 horse wheat reaper. Now that's some horsepower!
Why did they use so many horses? Were threshers really heavy or hard to pull? It seems weird, because now, we don't use much bigger tractors to tow and operate a thresher than we do for say ploughing or hay mowing.
Not that the machinery was heavy, but that the power needed was to both move the machine AND run it. Thus the reason for the mules to the mix - greater power was required. Thus the reason to add horses to the mix - speed was also required.
In short - horses work faster, but mules can pull harder and can work for longer periods of time. Mules work slow by themselves and won't be rushed, but will happily follow a horse at the same speed of a horse. Horses can be hurried along, and speed is of the essence when harvesting huge tracts of land.
Unlike a tractor, animals don't "operate" on a sustained level without rest. The large number of animals put to the machine allow for some rest periods (while still operating) for the animals in harness. They will simply back off the collar for a bit, get their wind back and muscles eased while their mates continue to work, then go back into draft. The more you have in harness, the easier the job is for all concerned, and the longer they can work before all are too fatigued to continue.
Keep in mind they had to stop to water them all periodically, too.