So I have 2 barns, made some good cow purchases, bred a bunch more and now have both at capacity, which I set to 12 each, they were breeding at 2/yr each barn. They should auto-slaughter any overages I thought, but instead of going over 12, the birth rate simple dropped to zero and no cows are being slaughtered for meat/hides, which was the whole point. My milk/cheese production is doing great, but those hungry villages are aching for hamburgers and beef steaks, and I just can’t supply them!
I’ve always upgraded my barns. Only problem is if you try to wall/fence them in. Sometimes cows get stuck in the barn geometry, which you fix by moving the barn, turning on/off grazing/milking and the cows move to the new location. You can then put it back.