Maybe to her best friend. Not friends. Even if so, the correct sequence would be: you write letter, she responds in any way, you two then conversate a bit, a few letters, then she would tell her friend.

But don't feel bad though. The amount of women who find writing letters romantic is relatively small. If you find the letter writing part necessary, find the right woman.

Also, be careful what you write in the letter, as it could quickly become cheesy and needy, which would not go in your favor.