It would work either way, as straw or hay, depending on the condition of your horse. If it's already round, I'd rather give oatSTRAW, if condition is needed, oathay.
If your horse is IR, and/ or has foundered before, or has tender feet, I would NOT feed the oathay, unless it's cut really late. The high sugar and starch content can trigger metabolic conditions.
Iv have fed oat hay that was in round bales early cut so was green. Horses loved it when it was really cold out but got to where they would waste alot of it.
Down side to oat hay my horses got fat as pigs on it we put out round bales so they free feed. My two palominos stick their head in the bale and never leave it. Only leave to drink water they both got really fat that winter.
Good oat hay is outstanding. It is often used as a cover crop for new stands of grass or alfalfa hay, and it has been my experience that kind (cover crop) is the best. If you live where it is moist - you don't want it to have come off of a heavily chemically fertilized field b/c it can, reportedly, significantly increase the nitrates in the cutting. I wish I could find some, here. They don't tend to like it as much as alfalfa, so it takes them longer to clean it up...but they do clean it up.