An advanced answer: yes you'll want to put animals inside a pen (previously animal zone), especially the herbivores who can eat free grass during warmer seasons (or all year round in a warm biome).
But you usually don't want your intelligent animals (usually carnivores) penned up, in case you aim to teach them hauling, which is super useful. If you restrict the area for an animal trained in hauling, then it won't help out with hauling.
My solution to this is: make sure all hauling animals get a sleeping spot. Then near that animal sleeping area, put up fridges containing throw-away food or suitable food. Stuff like kibble, raw "mystery meat", corpses or hay. Animals most often eat after they wake up in the morning, having slept on an empty stomach or gotten hungry over night.
Similarly, you could place such fridges in the outskirts of your human dining area, so that a hungry animal will go to the animal fridge before the human food. They only care about shortest path and make no difference between cooked food, raw food and kibble. They will however respect "do not use" status of a food item. And as for the humans, they will pick cooked food before raw.
Even if you have smart herbivores like elephants or thrubo that can be taught hauling, I wouldn't recommend training them for hauling/keeping them roaming free, because in addition to kitchen raids, they will also munch up your planted fields and orchards. You can still combat train them and keep them in a pen though, as long as you assign them to guard a human. When that human is drafted for combat, the penned animal will no longer respect the pen boundaries but come to assist, then go back to the pen once the human is undrafted. It might stop to raid the fields/kitchen on its way back to the pen, however, unless it finds some tasty grass nearby.