The Man
He is nobody in particular. Ovid addresses Book I and II to a man. In as much as men play a mostly universal role in relationships, while still maintaining the uniqueness of every relationship, all can be instructed through the same principles. So this man is you. He is the avatar of the reader who has come to learn about love from the master.
The Woman
Again, the woman is not a specific person. She is the reader. When Ovid writes to a woman in Book III, he is literally addressing the reader, assuming she's female. Whatever role each individual plays in their personal relationships, that's the one Ovid is talking about. In that sense, then, he could also be addressing those who identify with the feminine energy in a relationship. The same could be said of "him."
