Better late than never, I guess.

E. Willard Smith travelled West with Vasquez and Sublette along the Arkansas River in 1839. He gives us a great description of the two main methods of hunting buffalo:

Our hunters go out again today for meat. There are two ways of hunting buffaloes.
One called approaching, the other running. When a hunter approaches he puts on a white blanket
coat and a white cap, so as to resemble a white wolf as much as possible, and crawls on his hands
and knees towards the buffalo, until he gets within one hundred and fifty yards, then sinks his
knife in the ground, lies prostrate, rests his gun on his knife, and fires at the animal. It generally requires more than
one shot to kill a buffalo, even if he should be shot through the heart. The way of hunting
by running is on horseback. The man mounts a fleet horse trained for the purpose, rides full
speed toward the herd, and fires a light fowling piece, which he carries in one hand, while he
guides the horse with the other. The moment the hunter fires his piece, the horse springs out of
the reach of the buffalo to escape injury from the infuriated animal. This is the most exciting
method of hunting, but it is attended with consider able danger, the horse being liable to stumble
over the rough ground.

Here, Alfred J Miller's "approaching Buffalo" shows us a trapper and an indian approaching a herd.
The trapper (on hands and knees) is wearing a "wolf-eared cap" described by Smith.

Very nice

What would be considered a" light fowling piece" ?

A northwest trade gun, most likely. Light weight, when compared to a rifle, and about 20 gage in bore. The indians preferred them in general over rifles. Mountain men preferred rifles, unless running buffalos. The fowling pieces (or fowlers, or smoothbores in today's terms) are easier to load than rifles. They most likely shot under sized round ball with a little wadding (no patch) when running buffalo. There are stories of Indians carrying round ball in their mouth and spitting them into the barrel to reload.

Interesting Read

I've moved cows on horseback, once in awhile had to do some running on strays, always thought that would really have been something runnimg buffalo. The places I've seen that have buffalo use trucks, too dangerous to use horses

Any idea how far they went? Great uncle had an old trappers cabin on his property along Hayden creek a couple miles above the Arkansas. Built out of pine rather than quakey so it lasted a good while. Tore down by my cousin about 30 years ago. Uncle said it belonged to a cousin of Kit Carson. If they kept going into the mountains, past the royal gorge, looking for fur, I would be interested in any information.

This expedition traveled the Santa Fe trail to Bent's Fort (current La Junta, CO), then turned North to the post owned by Vasquez and Sublette, located on the "upper South fork of the Platte", roughly 50 miles North of present day Denver. From there, they travelled:

westward across the Rocky Mountains. Its route crossed the Cache a la Poudre
and the upper North Fork of the Platte and traversed the new or North Park of the northwestern
portion of the present state of Colorado and the northeastern corner of Utah. The pass used is
some two hundred miles southeast of South Pass. The ultimate destination of the expedition
and proposed winter quarters was Brown’s Hole. This is an amphitheater
shaped basin where the Green River emerges from the Wind River Mountains. The “Snake River”
mentioned is a small tributary of the Green.

A good many trappers went west into the mountains from Bent's fort, following the Arkansas to its headwaters and beyond.

I can't imagine what it would be like to be on a galloping horse, flying across the prairie amongst hundreds if not thousands of stampeding buffalo. A good number of indians, trappers and horses got injured or killed in the process.

Here's a general overview of the rivers of CO for reference:

I have always enjoyed the buffalo hunt depicted in the movie Dances With Wolves.

The territorial battles fought by the tribes to control the best buffalo lands was pretty interesting. Plenty of blood shed there. Blackfeet had an early advantage by their trade with the Canadians for guns, powder and lead. No love lost between the Snakes and the Blackfeet.

And what a game changer for the plains Indians the introduction of the horse was from wild herds escaped from the Spaniards. We tend to think of Indians and horses as always have been associated, but in fact just a couple hundred years or so of horse culture existed before the mountain man era. I have wondered about the moments that tribal people first laid eyes on horses and how they figured out to use them as transportation rather than just something new on the menu. Did they see a Spaniard riding one first to get that idea?

I think there is more to the story. Many Indian tribes were expert horsemen and breeders. How did they acquire that knowledge over such a relatively short time? Kinda like trappers wiped out the beaver and hunters the buffalo. To my mind its not that simple. Other factors had to be in play. Indians did not copy the European style of riding. They were expert tanners and leather workers. They could easily have made saddles with stirrups for example. Bits would have been a problem. I doubt wood would work very well. Hackamores were almost certainly being used by Europeans but Indians did not use them either to my knowledge.

Natives probably had a great handle on breeding from thousands of years of dogs. And if you spent every day of your life on horse back, I think you'd get good pretty darned quick. And there are references to indians using saddles in the journals and diaries, just not everywhere. I think its a case of it being somewhat common, so it wasn't mentioned much. But saddles aren't as romantic as bareback, so we have a skewed image of what really was. As far as beaver and buffalo, I agree 100%, the truth is more than we learned in school.

Here's a quote about indians catching wild horses, mentioning saddles:

The method adopted by the Indians for catching them is as follows: An Indian mounts a fleet horse, having a rope
twenty feet long, with a noose at the end, fastened to his saddle. He. rides close to the animal he
wishes to catch, and throws the noose, or lasso, over its head. The horse finding the noose over his head, jumps,
which chokes him and causes him to stop.

Here's a great description of an indian saddle, from John Bradbury's journal of 1809-1811:

an Indian saddle, which I shall describe. It consists of six pieces of wood: two of these are strong forked
sticks, one of which is formed to fix on the shoulders of the horse; the other is adapted to the lower
part of the back: they are connected by four flat pieces, each about four inches in breadth: two
of these are so placed as to lie on each side of the backbone of the horse, which rises above them;
the two others are fastened to the extremities of the forked sticks, and the whole is firmly tied by
thongs. Two strong slips of buffalo hide are doubled over each of the upper connecting pieces,
for the purpose of holding the stirrup, which is formed of a stick about two feet long, and cut half
way through in two places, so as to divide it into three equal parts: at these places it is bent, and
when the two ends are strongly tied, it forms an equilateral triangle. The conjunct end of the foremost
forked stick rises to the height of eight or ten inches above the back of the horse, and serves
to fasten on it the coiled end of the long slip of dried skin intended to serve as a bridle: this slip is
also made use of to fasten the horse at night, to allow him sufficient space wherein to graze, and is
mostly fifty or sixty feet long. Under the saddle is laid a square piece of buffalo skin, dressed with
the hair upon it, and doubled four-fold, and on the saddle the rider fixes his blanket.

Very interesting thanks for taking the time to share this information

That saddle sounds a lot what we use today when attaching paniers