To prevent animals from damaging hay cover, start by using cover materials that are tough, resistant to tearing and environmental degradation. Use a cover that's large enough to secure the whole stack and anchor it tightly to the hay stack to minimize gaps that animals might exploit.
Create physical barriers around the hay stack, such as fencing or netting, to deter animals from accessing the area. Regularly inspect the cover and the surrounding area for any signs of animal activity or damage, and promptly repair any breaches.