About women fighting in the middle ages... sure some did, but it's not like anyone was making female armour... they'd have to make do with men's armour. Just look at Jeanne d'Arc, nobody made her special armour because she was a woman.
Brienne is the perfect example of this as far as ASoIaF goes... if you want to participate in the male dominated martial scene of Westeros, you're gonna have to put up with wearing the same stuff as all those guys.
EDIT: I suppose Lady Mormont would get her own unique armour, but then again she's not described as the most feminine of women in Westeros, so I wouldn't expect anything that looks explicitly female.