The first time Little Dog (Jeffrey Hunter) and his party encounter Tanner (Robert Wagner), they are armed with repeating carbines. On all later occasions, they have bows until the very end when the rifles appear again.
The Army, at no time during the Indian Wars, used Winchester repeating lever action rifles, as shown.
When Appearing Day shows Josh Tanner how the Cheyenne were practicing for war, a camera shot shows several horses entering the fray. You can see that at least one of the horses has metal horseshoes, which would not have been the case in those days.