In the main thread you mentioned you didn't feel like you have enough, so I'm holding off on critiquing what you have until you get some more down.
So, you need to write more... Have you tried reading
this guide? It might help you analyze her personality and provide some ideas on why she acts the way she does, thus allowing you to understand and write more about her.
Why not take the individual traits and expand on them? For instance, if she's moody, why not write about what kind of lasting effect that has on her life? Does she recognize her own moodiness, does it bother her? Has it ruined friendships in the past, etc? How do her individual traits lead into and connect with each other?
You can also try setting some goals for her. Does she have a thing she wants to do? Become rich? Find meaning in life?
Okay, a little crit: she's a Book Child based off the story of yuki onna, so considering that she's lived her entire life in the City she couldn't have been stealing away children to live with her in the mountains. However, you don't have to exclude that completely. For instance, she may not ACTUALLY be a Yuki Onna, but since she's based on one anyone who had read those stories and legends might hold them against her. A potential prejudice against her is also something to consider when writing her personality and how she interacts with people. It may even have contributed to
her prejudice against the City People - we tend to act unkindly towards people who are unkind to us, after all.