There was a manga I read a while ago about a female lead who was originally either a queen or empress, who was killed by someone close to her. After she was killed, she went back in time and decided to look for her friend/pen-pal from her previous life. He was the Duke of the North I believe, and he was seen as a monster because he didn't have the normal “babyface smooth and beautifully handsome” face; he had scars and was more rugged. They also had this reputation of the female lead “taming the crazy beast of the north” and stuff. I do remember the female lead having pink hair, and the male lead had black hair and a black beard.
The main character reincarnates in a fantasy story; she uses her knowledge of the book and her past life to become empress, by marrying the handsome male lead, but divorces him because he's too possessive. Five years later, he kills her for this, and she reincarnates again in the past, in the same world.
This time she instead seeks out a man she never met in person but frequently exchanged letters with, and plans to marry him. As she's never met him, she briefly imagines what he looks like, and comes up with a typical handsome man from a romance novel.
His actual appearance is as you described.