We have been homesteading in SW Virginia, on a mostly wooded, mountain slope, and we've had to address the same questions.
We have dairy goats, chickens, and meat rabbits.
Feel free to dialogue via email:
david.mitchell.inbox@gmail.com
In brief, our goats love to eat bark, and they would probably kill all the trees if we let them roam free.
The chickens love the forest and forage for bugs under leaves, etc. They get too far away sometimes, and we typically lose them to predators (fox, hawk, bear) from time to time.
The rabbits we have in portable "rabbit tractors" and they mow the grass in our orchard, and fertilize along the way.
I'm not sure about other livestock.
We've kind of followed a reverse permaculture path, since we are starting with forest and working backward to open up areas for undergrowth and different layers. We keep propagating a variety of edibles and spreading them throughout. The deer are a constant battle though.