For archery, you need to remember that war bows were not calibrated for the minimum draw weight to be effective, but as strong as was feasible. The draw weight did increase range and penetration, but was well above what would be needed for a unarmored or lightly armored opponent. That and warbows were not the norm for most of the history and areas that bows were used in war, but were more of a later (and in some ways regional) arrival, and used by people who spend their childhoods training for them which affected their development into adulthood. lower draw weights were likely the norm for most of history.
For purposes of hunting a woman who has spent the proper time training (ie : regular training from a young age) would be able to get a higher draw weight to be lethal but it depends on the level or armor as high end armor eventually reached a point even war bows could not penetrate outside of hitting a weak point, and allot of areas did not get their bows to english longbow draw weights.
Though women being bow wielders does have a basis in myths, like the Amazons in Greek myths, but really being archers would not be for military effect, but to minimize the loss of females in war, and unless they had the funds to be mounted and heavily armored a rear guard archer would be safer and still let them contribute.
Of course keep in mind people supplied their weapons, and what would be easier for a woman to supply and have a chance to be familiar with other then hunting tools like bows and spears.