I was confused on Speight's movements and location. Bearss' article in the Arkansas Historical Quarterly (Vol. 25, No. 1, p.39) wrote that Speight was "en route from Texas to the Indian Territory". However, the original report doesn't say "from Texas", it just says they are on their way to the Indian Territory. [ORs, Series 1, Vol 22, Part 2, P.771, Steele to Baylor]. Bearss also says the capture of Speight's rear guard by Hart was southwest of Ft Smith, since he is assuming Speight is coming up from Sherman TX via the Ft Smith-Boggy Depot Road (the Butterfield Stage Route or Overland Road).
On August 8, 1862, Hebert reports to Sibley that Col. Spaight's [sic] infantry regiment was ordered to Little Rock. [ORs, Series 1, Vol 9, P.729-731]. I found a listing online of Co. E, 15th TX Infantry that lists a soldier who died at Camp Nelson, Arkansas on November 21, 1862. I also found a comment online that the 15th Texas Inf was the honor guard at Nelson's funeral in Little Rock. So... Speight was apparently at or near Little Rock and was coming up river to Ft Smith. Steele tells Speight to send back down river as many wagons as practical to get corn so it seems obvious Speight is coming up the Arkansas and the capture of his read guard must have been east or southeast of Ft Smith. Due to heavy snow, Speight has to stop for a few days. When he arrives in Ft Smith, Steele sends him on west toward Johnson's Depot on Canadian (south of present Eufaula OK) but learns there is insufficient subsistence there so he re-routes him south to Doaksville (present Ft Towson, OK) near the Red River.
It does see that Hart was operating out of the Choctaw Nation and/or along the border (e.g., Sugar Loaf). The Poteau near Ft Smith is in Oklahoma (Choctaw Nation), of course.
Ken