All of them except Norway have restricted the free education to EU/EEA citizens, I believe. University is still free in Norway for anyone of any citizenship, although even there there is some kind of requirement to prove ability to sustain yourself (might be possible through part-time jobs). Denmark, Finland, and Sweden have all introduced tuition fees for non-EU citizens, about €8k/yr in Denmark.
However I don't know what the situation is if you receive asylum. You might be treated as domestic for education purposes in that case, since it would be in the state's interest for people granted asylum to get an education and increase their employability.
Scandinavia and Iceland are pretty much the world leaders with respect to women's rights now, and have a keen interest in their public welfare, so if I were a woman without any form of family support, in fear for my life thanks to a tradition of honor murders in my native culture, I'd rather be there than anywhere else in the world. Even if people frown at you because you're a stranger, at least they aren't killing you because they know you too well.
However I don't know what the situation is if you receive asylum. You might be treated as domestic for education purposes in that case, since it would be in the state's interest for people granted asylum to get an education and increase their employability.