The Duke never dressed in period clothing once he started headlining.
As an example, he didn't like the look of suspenders on him, so he insisted on trouser belts decades before they came into general use for men, while John Ford put his Cavalry Troopers in cute little fireman-shirted, white-hatted, bandanna-wearing photogenic outfits, rather than campaign clothing, and put Officer's epaulets on shirts, where they were never worn - because they looked good on film.
God alone knows what the Sioux were doing, chasing 'The Duke' around the Comancheria and Apacheria, too...
If you're looking at the 'John Ford Reference Library' for historical accuracy - you picked the wrong place.
Plus - it's only a movie - someplace to forget about the day's events with mindless, air-conditioned, popcorn-fuelled entertainment.
Scouts Out!