There's plenty of hints that women in Westeros are more important than we give them credit for. There's this soon to be published novella, the She-Wolves of Winterfell that from the title alone, seems to imply that things have not always been 'handled' by men, even in Winterfell. We have examples of the Mormonts women, who are fierce fighters and have no husbands that we know of. The spearwives, are exclusively women as well, and, from Ygritte's own words, it seems that knowledge is passed down from mother to daughter amongst them. We know that the fathers blood and titles matters little to wildlings but it's possible that some of the wildlings clans are matriarchal. In Dorne, women inherit just as well as men. Balon Greyjoy preferred his own daughter over his son - Asha believed herself entitled to become queen of the iron island. This might well be an exception, but I don't believe that such things happen, 'just like that'. I believe that Balon's trust in his daughter's abilities shows that there has been precedents in the Iron Island's history, were women have played an important role. If every man and woman is shaped by his own society, a child of his/her 'time', then I think it's logical to believe that other women have paved the way for Asha. There's women like Olenna Tyrell, as well - one can argue that she's not the 'Lord' of highgarden but she is the de facto ruler of house Tyrell. And Melisandre, is a rather important player. Just as Sansa could have immense power at the tip of her fingers, were she only to reach for it. The 'cultural norms' are clearly not so well defined since all around Westeros (Dorne, beyond the wall), and inside Westeros (Highgarden, Bear Island) women have been powerful. I wouldn't dismiss women that quickly, especially since GRRM has made a point of killing off a lot of the young men in the 7K.