I think there are at least two aspects of this,
1. Having and raising a family
This I think this needs to be in the game at a mechanical level anyway, because we're also talking about things like animal husbandry and wildlife having young. It would also be nice to see this for the NPCs; to see children in villages grow up and for them to bond with other village members and also have babies. So ultimately what we're talking about is implementing some life cycle system to the game, which would also apply to human NPCs, and then would also apply to the player. The player should be able to do it, simply because NPCs should be able to do it.
You would find a mate, divide responsibilities, and then I think like others have said, the only real way to manage the baby is for it to happen all of the sudden because there's no good mechanic for it. Perhaps a chance that the wife gets pregnant if you're sleeping in the same room, with the chances going up the more time you spend together, or depending on some emotional relationship between the two of you that is tracked by the game somehow (such as the game determining if you're angry with each other or in positive relations, though I'm not sure how exactly that would be tracked). Then the pregnancy would come to term and there would be a baby.
2. The ceremony
This would be not just finding a mate to bond with, but having some type of ritual to mark the occasion and seal the bond and officially make you married. Generally speaking, I think it would be nice to see things like village festivals and festivities in the game. I can't speak much to what went on in Iron Age Finland, so I'm just thinking of what might go on in a Medieval village, where you might have some festival decorations like wreaths and garlands, and feasts, and music, and singing and dancing. I've been looking at old shepherd's almanacs, and the winter months after the harvest are set aside as a kind of feasting period. Then by May again, you get allusions to festivals again with May wreaths and so on.
The point being that right now it seems that there's no real social life to villages. Like a lot of things in the game, it feels villages exist to be primarily instrumental to gameplay, which is not the wrong focus for the start. But things can be expanded to make villages feel as if they have a life of their own, and then bringing the same mechanics for NPCs to the player also makes sense here.