Good ventilation and air circulation will mitigage moisture buildup under hay covers. Start by stacking the bales loosely, leaving small gaps between them to allow air to circulate. Choose breathable or vented covers, or leave small gaps around the edges of the cover to allow moisture to escape.
Elevating the hay on pallets or supports can also help by keeping it off the ground and reducing the risk of moisture absorption from the soil. Avoid sealing the cover too tightly, as this can trap humidity and lead to condensation.
