Dude, out here in the big prairie states where huge acreage and large animal operations are the norm, farmers don't fool with the standard hay bales. They make massive round bales, which are cylindrical and weigh up to a ton each. Their shape means they shed rain easily, so they don't need to be covered. The outer layer may rot, but there's plenty of good solid hay tight and dry inside. It's not unusual to see bales on the edge of fields that were made over a year previously.
They're usually 4-6 feet tall, and are moved with a truck (hooked up and dropped on the bed) or by an all-terrain vehicle used as a skid loader. They're usually left in the fields where they're made. Farmers haul them in as they are needed.
It's leaving them out in the fields that makes them easy targets, especially the bales that are on the sides of a road.