"Have you been able to match Osage from the 2nd IHG with names in the 9th KS Cav? I suppose these are those that 'went on a buffalo hunt' and were dropped from the rolls of the 2nd IHG, right?"

Not yet. I suspect there won't be much bleed-over. I'm early into all this, but from what I can tell, the 9th Kansas were the boys educated at the Osage Mission school as well as some Little Osage lead by Little Bear, one of the chiefs. At that time, the Osages were divided up into three larger super-bands: the Little, the Big/Great, and then the Arkansas band (who constituted the chief amount of Osages allied with the Confederacy).

"I'd be interested in other involvement of the Osage. Have you found them in other units or mentions of them informally attached?"

From what I can tell at this point, they were only formally involved in these three units: the 9th Kansas Volunteer Cav USA, the 2nd Indian Home Guards USA until late 1862 (where as you mentioned, they up and left the white men to their war), and then the Osage Battalion CSA under Major Broke(n) Arm.

There's also this oblique reference in a letter from Col. William W. Phillips (3rd IHG) to Gen. Blunt, December 25, 1862, Near Gt. Gibson, C.N.:

“The forces of General Cooper have been reorganized and partly clothed. General McIntosh is up the Arkansas, about 20 miles above this, with his regiment and 200 Osages. He refused to obey General cooper's orders to join him on the march to Cane Hill before the battle of Prairie Grove. Cooper has Worten's [Watie's] regiment, said to be 600 strong. It is scattered over the Nation in parties...”

Now, is that the same group as the Osage Battalion or some other Arkansas Osages who were informally attached to McIntosh? I don't know. I haven't been able to find a lot about them, yet. I hope in time that will change.

But as I mentioned, I'm very, very early in all this research.

"Who were the Osage with John Mathews at the beginning of the war? Can they be identified later in Confederate Units?"

I haven't dug much into this or the broader context of the bushwhacking and guerrilla warfare endemic to southeast Kansas and southwest Missouri during the war and its impact and involvement with the Osages who lived there. Once I get a handle on the timeline of the military units, I'll circle back to dive into the broader impact of the war on Osage civilians...

All that said, I have identified Augustus (Ogeese) Captain as being involved in John Matthews' raiding. He was was very vocally sympathetic to the South and soon mustered into the Osage Battalion as Captain of Company A.

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In the initial web searching that lead me to this forum, I've stumbled across a couple posts of yours over the past couple years where you mentioned some odds and ends of dispatches and the like found in primary sources. Could I chat with you some about that?

Email me at wp@willphillips.org if you'd be so kind.