Farm animals do not go inside at night, nor when it rains. They are outside all the time, apart from going inside the barn/coop to eat. Both the barn and the shed are on my farm, inside the fenced area
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My animals stopped eating all together and I found that they don't count as "in the coop" or barn after a while. (If you try to buy a new animal it will say 0/0 in coop/barn) If they don't belong to a barn or coop they stop eating and without food they can't be harvested. They also get sick EVERY SINGLE DAY regardless of brushing, petting, and poop collection. I have to sell and rebuy animals every time they don't belong to the buildings anymore.