Yeah they won't haul that automatically. Some things I do:
Train animals or use hauling robots, who mostly sort it out for me.
Go 'you are all useless' and crank everyone's haul priority to 1 for a couple of hours.
Play with one of the mods that add children. Make the children haul as a priority. Enjoy the idea of a child carrying around a dead cow.
You could also have your animal handlers (who I believe will do the slaughtering) haul as a priority, but I never have pawns I can waste on hauling.
Train animals or use hauling robots, who mostly sort it out for me.
Go 'you are all useless' and crank everyone's haul priority to 1 for a couple of hours.
Play with one of the mods that add children. Make the children haul as a priority. Enjoy the idea of a child carrying around a dead cow.
You could also have your animal handlers (who I believe will do the slaughtering) haul as a priority, but I never have pawns I can waste on hauling.