She drinks because it numbs her and numbness is better then cold.
She knows people judge her but she doesn't give a damn, because they don't know what it's like to have ice written in their blood and snow spread out everywhere they stepped. They don't know what it's like to have everything preserved, to feel cold and be cold because that's all you can be.
When she closes her eyes she can still see it, you know. She can still see the snow on the hearth and in her mothers eyelashes; she can see it outside the window and on her fathers hiking clothes. She can see how the bodies pile up on it, but none of them rot; she can see how red the blood is - how it leaks through the white, staining it - but the snow doesn't melt and the blood doesn't leave, and it stays like that - bright and red and sticking to her face and her fingers and her clothes, and it doesn't matter how hard she screams or how much people wipe it off her - it's still there, cold and red and unmelting, sticking to her mind and her heart and her soul.
No matter where she runs and how fast, she can't outrun it - because it's written in her name and in her blood; and in the end you can never melt them. Never.
So she drinks, and she drinks some more - because when she does she can't feel the icicle in her spine, preserving loss and pain.
She'd rather feel nothing then cold.