Cooper and Hawthorne woman in their writing

Cooper's women become progressively more complex, more active, and more realistic. Despite their potential of actual positions as victims, a number of young women are spirited, independent, and both morally and physically courageous.

For example, Bess in  The Pioneers lugs a canister of gunpowder up a mountainside to help Natty Bumppo, is consequently caught in a fire, and behaves with courage and dignity. Cora, in The Last of The Mohicans, is consistently praised by Natty, by Duncan, and by her father, for her wisdom and bravery. Finally Judith, in The Deerslayer, heedless of her own life, actually walks into a hostile Huron encampment in an effort to save Natty Bumppo from torture by fire.

As far as Hawthorne is concerned, Hester, in the Scarlet Letter, is not transformed or renewed in any way by her punishment or this experience aside from her physical appearance.  She loved a man who was not her husband, and despite her public ignominy she loves him still.  Unlike Dimmesdale, it's clear Hester would have committed the same sin/crime of adultery with Arthur if she had been given the chance.  To that extent, then, Hawthorne portrays her as an independent woman, beyond the morality of this Puritan town.  The people change how they see her and interact with her, but she is essentially unchanged from beginning to end. 

In drawing his admirable, spirited and intrepid women, Cooper not only depicts the courageous character of American women, but also symbolizes the potential of the new American settler. Whereas, when we think about what Hawthorne actually wanted women's role to be, I think we can say that he condemns the Puritan world of his novel, but at the same time, he did not necessarily want to overthrow a patriarchal system that gave men the power in this society.