I haven't gotten far enough to build coops, stables, and barns, but from what I see in tutorials you can't see the animals in them. I did see a horse in a large stable on LiF Wiki so perhaps part of what I about to say is coming.
Correct me if this is already a feature, but I would love to be able to see the animals I place appear in the empty slots in stables. I'm not saying show every animal you store. But, say you store a cow in a stable. A cow with small animations like eating and laying down would appear in an empty slot. Then you add a horse and a horse occupies the next slot. You can continue to add animals until all slots are filled by the corresponding animals. Once the slots are full you can keep adding animals until the stable's capacity limit is full.
The same can go for barns. I was so hoping to take a break from working the land and visiting my sheep and piggies in the barn. Maybe, even sheer the sheep by hand instead of doing it through a menu. I know sheering might be asking too much though. As for coops maybe there could be a few chickens or a rooster roaming a few squares around the coop.
It would also be great to allow some animals to go out to pasture. A pasture can be a new "building" that allow the animals to eat grass. Have one with a fence and one without. I mostly play solo and I really want to start an animal farm. Building a barn and stable is no small task, which is fine. I like the challenge. But, it would be nice to be able to start off with a pasture and maybe a tiny primitive shelter made of branches and clay that can be placed in the pasture.
Of course there would be consequences of having animals in the open too long. They could die of exposure if severe weather conditions were implemented. Wolves could get to animals in pastures/settlements without walls or fences. Perhaps we could have pets like dogs who could protect pastures. They could even protect players when they go out into the wilderness. I also brought up other ideas for pets in another thread here: http://lifeisfeudal.com/discussions/question/tame-animals
All of these things would add much needed life and challenges to the game. Especially for people who play solo or with a small group. Life back then was hard and it seems to be the games goal to simulate that. These are just a few ideas i have to make the game seem all the more realistic.