Tarps are expensive, and hay bales are comparatively inexpensive.

That said, I’ve seen farmers use old billboards as tarps in the past. Otherwise, it’s usually either a barn or a plastic sheeting.

If hay is stored outdoors in a typical temperate climate without a tarp, it's just a waste of everyone's time. Sure, cattle or goats can eat it, and it will make a turd, but the nutrients are gone within a few months.