to us, the three corner cocked hat is emblemic of the Revolution, and maybe the French and Indian, 7-years war, and the early Napoleonic days...but the reality is that the style was widely adopted by individual soldiers and smaller local militias of the Civil War.  The South had many examples, perhaps because the war was widely sold to the public as a second revolution to protect "the Constitutional right to property" (it's slavery, we can say slaves here.) 

anyway there were many ways to fold a hat up, some were strange, some caught on and evolved into the front folded up style seen in the later west. Here is a Massachusetts example. http://www.loc.gov/pictures/resource/ppmsca.31458/?co=civwar