I actually thought that Snow didn’t know either. I am not so sure. In Ep 7 in her letter to the queen it seems like Snow knows, but she may be talking about something else like getting between Regina and her father. I don’t know.
This is the letter:
“Dearest Stepmother,
By the time you read this, I will be dead. I understand that you will never have love in your life because of me, so it’s only fitting that I’ll be denied that same joy as well. For the sake of the kingdom. I hope my death satisfies your need for revenge allowing you to rule my father’s subjects as they deserve with compassion and a gentle hand. I know what you think you’re doing is vengeance, I prefer to think of it as sacrifice for the good of all. With that in mind, I welcome it. I want you to take my last message to heart. I’m sorry and I forgive you. “
It is just Snow talks about the Queen never having love in her life because of Snow. And how the Queen thinks of this as vengeance. And we know that Snow is aware that the Queen is trying to kill her. I just am not sure if the note makes sense unless Snow knows.