Probably Confederate infantry attire would strongly resemble British or French kit, to include either the Adrian, or, even more likely, the Brodie helmet.
One imagines that the Union would take its cues from the Germans, or, even more likely, the Russians, meaning either no helmet, or else some version of the stahlhlem. It’s also possible that one might see a distinctive steel hat more akin to the M1, or even a kind of “stovepipe” or “top hat” in steel.
I’m trying hard to think up certain National Advantages. Perhaps Confederate cavalry would be able to execute a kind of blitzkrieg. Would it be likely that a nation without much native automobile production, but having to cover a long border with a relatively small standing army, would develop a heavy emphasis on motorization?
As early as Bull Run, both armies were learning the military value of railroads.
