In the opening scenes, McDonald Carey is wearing a dark brown rimmed hat. When rides out of the Indian village and into town with Will Geer, he's wearing a cream colored rimmed hat.
The opening description and firearms set the time period at 1866. Jim Bowie died in the Alamo fight in March of 1836.
The exteriors were all filmed in Arizona, but the Comanche was a Southern Plains and northern Texas tribe. The costumes are also strictly northern Plains Indian designs not southwestern. Mixing cultures and locations was very common in this era of western filmmaking because they resulted in more picturesque and colorful visuals in their cinematography.
It's funny how Katie Howard (Maureen O'Hara) speaks with a strong Irish accent, while her brother Stacey Howard (Charles Drake) speaks with no accent at all.