Unless there's a mechanic I'm missing, it looks like the only way to feed animals (outside of natural plant growth in their pen) is to put a stockpile or shelf in their pen/zone for storing hay/kibble/etc., which has some flaws if you want to also keep some of that animal feed in your main storage for other purposes, or keep different animals in different pens/zones.
There should be an Animal Feeding Spot building that can be configured with allowed food types and a target amount. Pawns with the Handling or Hauling jobs will automatically bring food to the Feeding Spot until it has the target amount, and animals will prioritize eating from it. Each feeding spot can also be assigned to specific animals.
While the Animal Feeding Spot is constructed or deconstructed instantly like the other "Spot" furnitures, there could also be some improved versions that require materials and work:
- Animal Food Bowl: Nullifies the ugliness penalty from having food lying around, and gives a mood bonus to the animal's master if it's well-made or made of beautiful material.
- Animal Feeding Through: Acts like a cheaper, more specialized shelf - it can hold more feed than just the ground, and prevents degradation.
- Refrigerated Feed Dispenser: Similar to the through, but if it's powered, it'll prevent feed from spoiling. If it loses power, animals are unable to eat from it.