Besides performing the normal household functions of producing, preserving and preparing food and clothing for the family and taking care of the children, Iroquois women participated in many activities commonly reserved for men. They gambled, they belonged to Medicine Societies (spiritual associations) and they participated in political ceremonies.
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As I understand, The Council of Grandmothers was a unique final solution to power struggles and decision making. Their version of the US "checks and balances".
No major decision could be approved without the review and consent of the Grandmothers.
Reasoning, again as I remember, was that they had given birth, nurtured, raised the children of the tribe. They were not driven by testosterone or the follies of youth. They always had the long term good of the clan in mind, for survival.
Maybe I missed something on your "role of women in ..... ", if so I apologize. If not, please add more about this.
They would raise the children and declare wars. Also, they would do most of the cleaning and cooking. Some were even chose as the clan mother which is kind of like a mayor, and they make most decision's.