Thanks Danny! That is much more than I had found.
I had completely forgotten about the book "Polignac's Texas Brigade" by Alwyn Barr.
The dismounted cavalry were under Bradfute, Roane's Div, at Prairie Grove.
Colonel Speight went ahead to meet General Steele as the brigade neared Fort Smith. In his absence on January 13, a band of Union guerrillas struck the Confederate supply train by surprise, disarmed its small guard detail, and captured much needed corn and some of the better wagon stock. Most of the corn was quickly recaptured, and Lieutenant Colonel Harrison of the 15th Texas pursued with ten mounted men and a company of infantry on January 14, covering over thirty miles through snow. He located the raiders but could not close with them because they were mounted. Texas cavalry under Lieutenant Colonel R. P. Crump solved that problem soon after their arrival next day by capturing the guerrillas including their captain, Martin D. Hart, a Unionist and former state senator from North Texas, who was hanged on January 20 for the brutal acts of his men against civilians in western Arkansas. p.14
I am particularly interested in their movements in the Indian Territory under Steele. Though they didn't see any "action" in the Indian Territory, their movements and accounts provide information about the IT that doesn't exist elsewhere. I began studying this brigade while trying to decypher the locations of "Canadian Depot (Johnson's Place), Camp Johnson, Johnson's Depot, Johnson's Station, Johnson's and Johnson's on Brushy [Creek]". Correspondence between Steele, Cooper, and Speight use these names and it appears switch the names at times. I believe that Canadian Depot, Camp Johnson, and Johnson's Depot are the same place near the Texas Road on the south side of the Canadian River (south of present Eufaula OK). I believe "Johnson's on Brushy" and Johnson's Station are the same place and the same as Blackburn's Station on the Butterfield Road (aka Ft Smith-Boggy Depot Road or Overland Road). However, I think Steele at times calls Johnson's Station "Johnson's Depot", adding to the confusion.
I believe, and am trying to confirm, that Steele sent Speight toward Cooper's headquarters at Canadian Depot/Johnson's Depot/Camp Johnson on the "south side of the South Canadian" but learning there was insufficient subsistence there he reroutes Speight via Blackburn's/"Johnson's on Brushy" on the Butterfield Road and hence to Doaksville where Speight establishes Camp Kiamichi at the mouth of the Kiamichi River on Red River... all in the Choctaw Nation.