LOL - I dunno.... If it were really about native costume, then the Arabs would have stuff hidden under their robes too...
The modern Jordanian Desert Patrol (we're not talking arabian-nights-era) wears a modern grayish police-type uniform, with the rifle slung over the shoulder.
I almost thought we had a costume class in dressage when a woman showed up in a Michigan State campus police "mounted division" uniform. While police and military can ride dressage in their riding uniforms, I pointed out to the TD that Michigan State campus police does NOT have a mounted division, so her "uniform" was a fantasy piece. In fact, it was all black, and looked surprisingly like a nazi SS uniform.
The TD took the line of least resistance, and allowed her to ride in that uniform. It was an embarrassment, IMHO.