I recall reading that by 1876, in the field, the officers of the 7th Cavalry generally wore blue shirts, with collars variously embroidered. the soldier's also largely dressed as they pleased, in a mix of their fatigue dress etc.
Here's the customary image of the US Cavalryman in those campaigns, based on the old Hollywood movies.
But the descriptions of 1876 imply the average trooper just wore the G.I. issue GRAY flannel undershirt, or any kind of shirts, etc.; the trousers frequently heavily reinforced in the inseam with canvas for hard wear on campaign, and the 1870s campaign hat was black... Also looped canvas cartridge belts were generally employed in the field instead of the regular leather accoutrements.
Well, realistically, they´re in the middle of nowhere - virtually the only people around who weren´t Native Americans. Who was going to mistake them for anything but soldiers?