I used to have a vintage woolen Wehrmacht coat. It didn’t have any insignia or markings, but when I visited East Germany (and it was still East Germany then) I was advised that people would recognize it and react… unfavorably. For whatever reason it was unremarkable in West Germany, but before crossing the checkpoint I had to buy a dopey-looking fake down jacket.
It was a very sturdy coat, and warm! I mean, I wouldn’t want to besiege Stalingrad in January wearing it, but it was great for winters in civilized places.
Not that I’d want to besiege Stalingrad under any conditions.