Does anyone know the name of this children's novel?

I am trying to remember the name of a children's novel that I read somewhere between the ages of eight and ten, but my memories of it are very fuzzy. It was rather dark compared to most books targeted for this age group. It is about a girl who lived on the West Coast with her father for most of her life until he dies suddenly. She moves east (to Vermont, maybe?) to live with her mother whom she barely knows, and becomes attached to a dapple gray horse that she names after her favorite character in a CS Lewis book. The book is basically about her caring for this horse and trying to mend her broken relationship with her mother. That's about all I remember, except for the fact that the cover was red. If anyone remembers the name of this book, or a database that might help me, I would greatly appreciate your help.