From Lakota America: A New History of Indigenous Power, by Pekka Hämäläinen (The Lamar Series in Western History; Yale U. Press, 2019), Kindle pp. 153-154:
Lakotas stayed out of the War of 1812, but the war years were a dynamic time for them. There were exhilarating advances in equestrian technology: several winter counts record how Lakotas captured their first wild horses with lariats somewhere in the western plains. The practice signaled a larger expansion of the horse culture across the grasslands. Herds of wild mustangs had multiplied in the southern plains to the point where animals began spreading into colder northern latitudes, and Lakotas may have adopted the use of the lariat from their more experienced Cheyenne allies.
There were also far-reaching political developments. Lakotas fought with Crows in the west, clashing over horses and hunting rights, while also engaging in active diplomacy with Pawnees and Kiowas to the south. The talks were often tentative, rendered so by the very dynamism of the rising horse nations of the plains. Comanches, Kiowas, Crows, and other plains nomads were now rapidly accumulating horses, their ambitions growing along with their herds. They were jockeying for position in the western steppes, competing for the richest hunting grounds, the best riverine pasturelands, and key trade corridors.
Though still bound in the Mníšoše [Missouri R.], Lakotas were not exempt from these rivalries. Most of their oyátes had begun regular bison hunts in the West where, at the edge of the Black Hills, they sometimes wintered with Cheyennes. The western excursions drew them into conflict with Kiowas, who were in a habit of traveling to the Black Hills from their southern homelands around the Arkansas, where they lived in an alliance with the powerful Comanches. Lakotas could ill afford a war with Kiowas, who had become prominent middlemen, carrying Comanche horses to the North Platte where they traded with Cheyennes. In 1815 a Lakota delegation traveled there to hold a peace council with Kiowas. It went badly. A Kiowa tried to steal Lakota horses, and a Sicangu warrior buried a hatchet in his head. Lakotas drove the Kiowas all the way into the Rockies. It was a major event, recorded in numerous winter counts, for it anticipated Lakota expansion into the West.
Lakotas were not plains nomads yet. They ventured into the grasslands to hunt and trade and raid, but they did not feel safe out in the open. They were still building up their horse herds, and the Black Hills were dominated by Crows and Cheyennes who commanded the western grasslands from the rocky bastion. In around 1815 Sans Arcs astonished other Lakotas by building dirt lodges at Peoria Bottom above the Bad River. They then did something even more unexpected: they built large wooden houses, which they occupied for at least two years. The pictographs of the boxy structures appear at once cozy and utterly alien on the buffalo hides.