The Hay Hopper is a tool. It is included with your Barn or Coop when you purchase it, and is used to move Hay from your Silo to your inventory. It’s used as a quick way to fill up the feeding troughs in these areas to feed your animals. You are also able to put Hay into your Silo via the hopper.
If you have the Deluxe Barn or Coop, you will not be able to use the hopper to retrieve Hay because it is automatically added to your feeder. You can, however, still deposit Hay through the hopper.