We don’t really know much about who this man was. Wynne doesn’t say much about him. The only narrative we really have in the game about Wynne’s pregnancy is her very brief account:

Alistair: So you… mentioned you had a son? What happened to him? Wynne: I honestly don’t know, Alistair. He was… taken from me. Such births are seldom, as there are ways to prevent it, but it does happen. And any child born to a Circle mage belongs to the Chantry. Alistair: I… didn’t know. I’m sorry. Wynne: It’s all right. It was a long time ago. A very long time ago. Alistair: Couldn’t you do something about it? Wynne: Do what? I was weak from the birthing process and there were… no, there was nothing I could do. Alistair: Do you think about him? Wynne: All the time.

This account, however, conflicts with what the father of that child had to say on the matter, found in a letter Wynne kept among her possessions. (World of Thedas, vol 2, pg 89)

It’s a good thing we haven’t spoken much since my return. Anger put my mind in disarray and civility would have been damn near impossible. But it is time, and perhaps in writing, I can put into words what I find difficult to say in person. 

You told me you had no choice but to let them take him. Tell that to yourself if you must; we both know it isn’t true. You had a choice from the very start. From the moment you found out. But you withheld knowledge of my own son from me because you knew I would have found a way. You knew I would have given up the Order for the both of you. So blame my love for the Chantry, the templars, my vows, if it helps you live with it. Maintain the fiction that you couldn’t drag me down with you. Pretend that you are the martyred party. I’ll always know the truth; you chose your place in the Circle over your own son. Your belief that perfect obedience could win a mage the trust of the Chantry was more precious to you than what we had. You decided to be helpless when you had a choice to fight. It wasn’t your decision to make. He was mine, too. The Chantry may have taken him, but you kept him from me.

Honestly this letter breaks my heart. We don’t really know how Wynne felt. Maybe she was in love with him but was too afraid to run from the Circle. Maybe she didn’t consider him more than a fleeting affair and wouldn’t have wanted to run off with him even if he could protect her and Rhys - though that’s a pretty cavalier attitude for a mage to risk a relationship with a templar that is only a fling, as it could ruin both of them if they were caught. We do know she cared about him enough to never reveal who he was, even when she was being pressured by Enchanter Wenselus. She didn’t want the father of her child to get into trouble for involving himself with a mage.

But there is no question that he was in love with her - so in love that he would have abandoned his life’s work and run off with her. He’s clearly angry in this letter, which is completely understandable, considering the circumstances. He had a son with the woman he loved only for her to choose the Circle over both of them. It is not as though it’s an easy choice - the two of them would have been forced into hiding in order to keep their family intact. Wynne would have been an apostate - something she’s never shown any desire to be. But it was still a choice. She had support. And the father of her child would have had the ability to secure and destroy her phylactery. She had a real chance to live a different life and she chose not to.