In its first two seasons, "Game of Thrones" established that it is a series that features some of the strongest female characters currently found on television. Although some of the older women understandably get a lot of the press, the young character of Arya is also a tremendously strong character who has shown time and again that she has a core of iron.
Indeed, from the very beginning of the series, Arya shows that she is not going to put up with the same sorts of nonsense that her sister Sansa is so willing to tolerate. Rather than bowing down to the restricting expectations that her culture has for women, Arya wants to be a warrior, and though her father is uncertain about the wisdom of such actions, he does allow her to begin training as a swordswoman.
It is this training that gives Arya the skills that she will need in the days to come. Faced with the execution of her father and given the fact that the rest of her family is scattered to the winds, Arya shows time and again throughout the first and second season that, like all of the Starks, she has a core of iron that allows her to survive trials that would have no doubt squashed a less stalwart character.
However, it is only when we get into the second season that we truly get to understand how incredibly strong Arya truly is. When she becomes a part of Lord Tywin's household, we get to see her shine, and it seems that even Tywin, the old cynic himself, can see the iron core that is a central part of Arya's character. Just as importantly, however, fans get to see her sharp intelligence as she manages to engage the formidable Lannister lord in some witty and sharp dialogue. Truly, this is a young woman who has more strength than many of the adult men that appear in the series.
As we can see, the strength of a character does not necessarily rely on either their gender or their age. Arya, her sister, and her mother make one thing clear: In a fictional world where women are often the political and sexual playthings of men, there is still the possibility that their strength can surface and that they can manage to carve out some measure of their own destiny.