I was a dairy farmer and had grade Holstein cattle. I bred my best cows to the best bulls I could find that offset the worse features of my cows and added some production.. but since the cows produced well (had a herd avg in the top 3% in the State) I was more interested in a structurally sound cow that would last physically.
I think that farmers and ranchers bred dogs and horses and cattle etc. the same way. They used the best they had.. and if the best horse was from a feral herd they used that horse.
The thing to recall in this is that the feral horses of the middle 1800's had mostly Barb blood and were really good horses. The Native Americans used them and while small, the outlasted the Government troop horses and were faster. The US Government actually put Draft Horse Stallions in the feral herds to water down the stock to something slower.. (per Dr. Deb Bennett's books and literature). The result is what we see today in the feral herds.. an occasional nice one (and there are!) and a lot of not so nice ones.
From my understanding and past reading, the Thoroughbred was added to the Quarterhorse to add speed and a more consistent type. Remember.. in those days there were no horse trailers, shipped semen, TV and so forth. That same little ranch horse was often called upon to be in a horse race on Saturday night.
Men and not a few women defined themselves by their horses! Status was to have a really good horse... it was prestigious to have a Thoroughbred in a place (Western US) where getting such a thing was rare. Those horses came from the East and some even from England. English Blood was known.. such as Imported Messenger who influenced both the American Thoroughbred AND the American Standardbred!
Horses were, in those days, the Rolls Royce, BMW, etc. of today. Most of the population was relegated to something much less as a ride.. and on some occasions, those "lesser" rides showed up at a competition and cleaned house.. and deals were struck and horses were bred.. sometimes in secret.
Most American breeds of horses go back to some unknown mare or stallion... and is many cases it was known... but not shared. Justin Morgan was such a horse... as was Hambletonian...
Interesting in your list of statistics is the number of Cleveland Bays and Suffolk Punch.. both now rare breeds because their usefulness has gone by the wayside. No one needs a Rangey tall Carriage horse that breeds both true to color and type to make matched teams and 4 in hands.. and no one needs a nice small compact draft horse like the Suffolk. I always liked both these breeds. I suppose the Cleveland bay was replaced in today's world by the more athletic Warmbloods and the faster racing Standardbred. The Suffolk just simply is not used.. always sorrel and not flashy.. so is not favored for any replacement 'sport.'
My breed of dog is the German Shepherd. I had one that herded cattle on my dairy farm.. and that dog had me fall in love with the breed. Sadly, that was years ago and the breed has segued into three breeds (American show, German Show and Working lines)... none of which are what that first dog was.
There is something about the outside of a horse that is good for the inside of a man. ~Winston Churchill
) Dinosaur Horse Trainer