Ideas
I am having the same issue. I opened an old save to continue playing with Cottage Living because I hadn't really played much yet and I had a llama in my shed. I played with the llama until it passed away and bought a brown cow. Then I had the same problem everyone describes. I could assign the cow to my shed but it then appeared greyed out and was stuck in household inventory. I couldn't place it anywhere in build mode. I finally was able to use debug to "create cow" and was given a spotted cow so it seems I am still able to use the shed, but my original brown cow is still stuck in household inventory so this is not much of a fix. If you are wanting to keep specific animals this doesn't help, however I wanted to share in case anyone just wanted to keep using the shed for gameplay reasons. EA should be ashamed of themselves to make this such a selling point of this pack and then ignore such a huge bug in the pack for over 7 months. Hope this can help someone.