Well, I could be wrong, but I believe Oprah wears a wig for her Trichotillomania. She has been trying to keep her 'Trich' a secret, but in her last interview, she confessed to her disorder.
I would wear a wig if I was bald and couldn't do anything to grow my hair.
Tell her its apart of a game you want to play with her or role-playing.
No
I read on one of her websites that for the film Atonement, she agreed to have her hair dyed red(ginger)