Wrong type of rifles used by U.S. cavalry troops
Hollywood is to blame for this frequent error of depicting U.S. cavalry and infantry employing Winchester lever action rifles during the post-Civil War Indian Wars of the late 1860s into the early 1880s.
The U.S. Army found itself with vast stocks of muzzle-loading Springfield rifles at the end of the Civil War, numbering in the hundreds of thousands. Breech-loading rifles and repeaters were entering military service the world over so these muzzle loaders were obsolete and essentially unsaleable. The U.S. Army declined General Sherman's proposal to adopt the excellent, single-shot, breech-loading Remington falling block rifle. Instead, the U.S. Army adopted the economical and practical expedient of converting numbers of muzzle-loading Springfield rifles to breech loaders. The resulting conversion was called the Allin Trapdoor Springfield rifle or carbine.
So in CHUKA, what we should have seen would be the U.S. cavalry troopers armed with with Allin Trapdoor Springfield carbines. The infantry held the rifle breech loader.
Others have pointed out some inconsistencies as well. The fort was grossly undermanned in the movie. The fort itself appeared to be extremely small, but this was due to the fact it was an indoor studio set. Also budgetary constraints probably had much to do with the small numbers of stunt actors employed as cavalry troops. From a historical standpoint, there would have been infantry stationed at the fort as well. There should have been artillery at the fort. There was not a single cannon or howitzer in sight. Whether there would have been a Gatling gun as well is open to debate. The U.S. Army did not purchase many Gatling guns due to the end of the Civil War and the great reduction in the size of the standing U.S. Army.