This is an interesting question. However, it is extremely broad. In other words, it is not possible to make generalizations. Therefore, the best way to answer this question is to examine cultures individually and see what women do. If we do this, we can make the following observations:
1. In ancient Hebrew culture, women played many important roles, even if men ruled for the most part. At times, women served as judges and leaders, like Deborah. Some were prophetesses like Hudlah in the book of Isaiah. Still other were powerful political leaders like Jezebel.
2. In ancient Greek culture, women again played many different roles. One of the greatest poets of the ancient world was Sappho. Women also played many important religious roles in the household and during state religious functions. Also if we take Plato seriously, one of the teachers of Socrates was a woman, Diotima. If we consider the Spartans, then women were even more powerful.
3. In Rome, women played even greater roles. There is much evidence of their power, influence, and ability to act in significant ways. Think of Cleopatra's role in Roman politics or Livia, the wife of Augustus.
In conclusions, women played many roles.