Help to find book about Charlotte/Charlie YA

I need help finding a book that I read a while ago, probably at least ten years ago. I borrowed it from my local library and loved it, but cannot remember the name for the life of me. It's a period setting, maybe later 1800's? The cover had a beautiful picture, half of a girl's face, half of a horse face, both reddish hair and blue eyes. The copy I read was hardcover, and it seemed a few years old.
The main character was named Charlotte, I think she lived in an orphanage, maybe her parents' home, but was getting too old be taken care of, and so was going to be handed over to the state or something. Before that happened, she climbed out her window and ran away. I remember clearly the description of her walking through ice cold water on her way. She disguised herself as a young teenage boy named Charlie, and eventually got a job in a barn. She described the painful process of binding her chest to look flat.
Somewhere along the way, she meets a specific horse, but I cant remember what the reasoning was, besides it being in the barn she was working for.
I feel like one of the other workers found out her identity, and maybe they fell in love?

Thanks for the help!

Ah, I had this book...I will see if I still have it. The cover was pretty memorable!