Can I ask a woman to remove her big hat during a movie screening?
Maybe. Why are you going to ask her to remove her hat?
I can't watch the movie with that big hat on.
She should have known that she was going to a movie theater, and that her big hat would interfere with other people behind her. I would ask her kindly to remove the hat on, and if she did not listen then I would recommend that you tell some staff members of the cinema to possibly remove her from the theater.
I could either pull the hat off or I could set it on fire.
No you should not do that. It is definitely better to let the movie staff handle it. But I can understand why are upset since it is not letting you enjoy the movie.