Moisture is the enemy of hay, so anything a producer can do to reduce the amount of moisture reaching hay will likely reduce losses. Protecting bales from rain that can penetrate hay is obviously desirable (bale wrappers help  in this regard). What is less obvious is that with most types of forage crops, the greatest losses to round bales stored outside result from moisture moving into the hay from the ground. Avoiding hay-soil contact is a highly desirable first step in reducing hay storage losses. For example, simply placing bales on old tires, pallets or a layer of coarse gravel will reduce loss. Forage-Livestock Quotes and Concepts, vol. 2 is available here.