The answer is: it is impossible to know for sure. While there are several legends about Viking women who acted as Shieldmaidens (the most famous being Brynhilda/Brunhilde from the Volsunga Saga), and those legends must have been based at least in some real events, there's not enough archeological evidence to confirm that. There are also some historic records about such women but more evidences would be necessary in order to reinforce their actual existence. For many years, when a female Viking skeleton was found alongside a sword or other kinds of weapons, archeologists usually assumed that the male skeleton from that particular grave was missing. And though it isn't necessarily the case, one can not assume that, if a woman was buried with a sword, she must have been a warrior of some kind. The opposite, however - that the woman was a warrior - also can't be discarded. What a mess, huh?
With the arrival of Christianity, it is possible that women in Scandinavia (where the Shieldmaiden folklore is more common) were strongly relegated to domestic chores for many centuries. I like to think, though, that there were some women who escaped this forced housewife role and kept practicing with their swords, bows, axes, spears or wathever they fancied, and, most importantly, passing that knowledge to their daughters.