Wheat Straw - Straw is used extensively in the Dairy industry to "cut" the protein on alfalfa and for its bacterial innoculation. Basically, it is like yogart, the good flora on the straw help the digestive system in the cattle. There is nothing wrong with feeding straw as a filler for your horses; straw quality is like hay quality - some is good, some is poor. Most guys baling wheat straw don't care as they are baling either bedding material or erosion control. And yes the dairy industry grinds the straw into a TMR wagon thus creating a "Total Mixed Ration" for the animal to eat. Many horses will eat straw, some may not - a lot of it depends on the quality of the straw.
Round bales are designed to be handled with a tractor, not by pushing them - it is very easy to bust a disc in your back pushing on a 800-1500lb bale of hay - STUPID!
Storing rd bales outside is not a big deal in the arid west or the north, this is not an option in the east or the south, we get way too much rain and our snows are wet, not dry.