OK, I did a google search - with pictures - on Orthodox Jewish women wigs.
I found nothing that covered the face.
Now if it’s a hat, then isn’t it standard procedure to remove all hats for mug shots?
Would they make a cancer patient on chemotherapy remove a wig for a mug shot?
Hookers (especially transvestite hookers) wear wigs and are required to remove them for mug shots.
My wig is not “wiggy” looking, it looks like real hair so how would they know it is not my real hair?