Yeah, Rosa thought of that immediately after her prior suggestion. But she could certainly have asked the prince to bring scissors on his next visit, and they could have escaped right away instead of waiting for her to weave a rope from balls of silk!

Also, absent scissors, what about breaking the hairs by hand, or by friction on a slightly rough surface? Individually or in small groups it should be possible though very very slow. But if you're captive in a tower, you've got nothing but time.