Amanda Sauer (now Amanda Sauer-Cook) wore the white hat for an Ohio State spring game.
Here is the link to that article about Amanda. She is now a center judge in the XFL and a part of the NFL Officiating Development Program.
As an aside, I worked a D3 game where the white hat was the wife of a current NFL official. I would not be too surprised to see more women in football, including wearing the white hat.