I've seen a Naval officer with a skullcap, in uniform, indoors. Outdoors is not a problem, you can wear whatever you want, that doesn't show. (there are of course exceptions to that as well.) Pretty sure he wasn't a chaplain. As to Cowboy hats...
Those are allowed in certain units and under certain circumstances. I was at a change of command ceremony a few months ago. The guys manning the Salute battery all had on Stetsons, with ACUs, brown boots, etc.
Sort of like this:
Although this was a much earlier ceremony, and that was the incoming Deputy CG, on the right and the Command Sergeant Major on the left. The CSM looks a lot more "at home" on the horse than the General. :)
You can see what is likely part of the same salute battery that I saw, over on the right in the background. That is the 1st Cav's battery. The ceremony I saw just borrowed them.
The Cav wearing uniform article directly related to US history is not at all the same thing. I meant it more like saying if you are Texan, can you wear a cowboy hat because it means sometining to you personally? Lke a Sihk with a turban.
It’s be un-American to hate the Cav.