To cover hay on a budget you'll want to choose cost-effective strategies and materials. The most effective way to save money is to minimize losses by protecting your hay from the elements. A high-quality hay cover may cost more at the outset, but it will save money when you can re-use it for several years. If you're concerned about wet winters with wet ground, raising the floor with pallets is a cheap, effective solution.
For many tons of hay, a good cost-effective choice is to assemble one or more affordable enclosed structures. For example, a car port frame with the tarps secured around the side will help minimize exposure to the elements. Be sure to anchor the building carefully against high winds! No matter what the choice, carefull stacking and good quality hay covers will save plenty in the long run.