Well, you would be wrong. The house belonged to the Lord, as did the land, the surrounding lands and so on. The very well could have said “no pets”, if they had cared. They had veto power on marriage, changing labors, and everything.
The Lord owned the serf in the same way that a homeowner owns the sidewalk. They had to provide basic protections or someone higher would eventually maybe get upset. They could do basically whatever they wanted to them, but the serf could only be sold as part of the estate.