This is my take on the subject....
Giving that I have both cowboyed on the same horse all day 12 hours and rode 12 head a day in the arena.
If I am riding horses in the arena and "training" on them, switching horses every half hour or so, I shorter stirrup is perfect. But when cowboying, I like a long stirrup, I let them out a couple of holes. There is a big difference between riding a pile of horses in an arena and staying on the same one all day, even if you if its the same amount of hours. A longer stirrup is much more comfortable for long hours and easier to rope out of.
Someone mentioned that the horses were smaller, yes they were, but so were the people. My father in law has a set of boots from a relative who was Calvary soldier from the Civil War(I believe, I might have this wrong) They are tiny! But that was the average size of a man back then. So I think the size of the horses may irrelevant. I think it was more of a comfort thing IMO.
The idea of a good cowboy back then was different as well. A cowboy was judged on his ability to ride tough horses and buckers and get the job done on that type. They bred horses for their hardiness, not its ease of train-ability. The horses were way tougher. Now it's different, good cowboys are considered by their ability to be a good cowman and horseman, to be able to make a good solid quiet horse while getting the job done. And we are breeding better horses, instead of riding these big feather footed broncs, they found out that riding a good mind horse is actually much more efficient. Work smarter, not harder.
I DON'T LEAD 'EM AND FEED 'EM, I RIDE 'EM AND SLIDE 'EM.