Hi,
Just adding my understanding into this as well, although I don't have a lot to add to the above posts. From what I've been able to gather, Samurai women were just as well trained as their male counterparts, just with a slightly different emphasis. From what I've seen, the use of the Naginata as a "womens weapon" is more from the Sengoku Jidai and Edo Jidai than the Kamakura and other earlier periods, mainly because in those times, the Naginata was primarily a battlefield weapon, and had a size and length that reflected that.
Later, as the Sengoku Jidai took over (and the men were often out at war), and then moving into the Edo Jidai (when there was the situation of Daimyo being forced to keep two separate households - one in their own domain, the other in Edo - and spending one year each in each home, but separated from their wives and children resulting a constant threat to ensure loyalty) there would be more cause for a Samurai woman to need to defend her home (from raiders/robbers/disenfranchised Samurai etc). At this time, the Naginata became lighter, with a shorter blade, more suited to woman's physical attributes. This made the weapon more manoueverable, and lead to many swordsmen not wanting to try their luck against a well-trained Samurai Lady with her blade. Even today, I understand that there are still competitions between male Kendo-ka and female Naginata-do players...and the men often find it very difficult to make it out in one piece!
But the weapon I have seen most associated with Samurai women is the Tanto in it's various forms (the Aikuchi probably the most common). Schools such as the Tendo Ryu Naginatajutsu still have a component focussing on just the use of tanto in their syllabus, and Tanto have been traditional wedding gifts for women in Samurai families. Their is even a different way of commiting suicide for Samurai women wherein the woman cuts her own carotid artery with her tanto (rather than the more familiar dis-emboweling of the men).