No. I've never heard of feeding any kind of straw to horses, bovines for roughage, mixed in the feedwagon yes.
Oat hay (green) yes, but it's rich, feed sparingly, like afalfa or grass/alfalfa mix, latter I've never had trouble with, fed lightly to supplement, but straight up alfalfa, way too rich and risky, besides they get fired up on that rich stuff, makes em hard to deal with.
Good quality 1st cut, 2nd cut hay grasses, or a mixture of both 2x-3x per day, and suitable grain or equine feed 2x a day has been the standard for as long as I can recall, well around here at least. Mind you, these are working horses, things change when they are off due to weather, season etc. Good hay will suffice them.
Most use bagged, grain mixes or pelletized feeds, but when I was a kid we had none of those, and all the supplements and all the other "jazz" it was whole oats, crimped oats, and or a sweet feed, that was some mixture of grains with molasses, it came in burlap bags, which changed to weaved plastic bags later.
We prefer to keep em or as many of them as possible on grass in the spring summer/fall, reducing other feeds like pelletized or grain mixtures, some get supplements. I am a firm believer that grass is best, followed by good quality hay, 1st/2nd cut grasses, (when can be found/afforded) They do fine on good hay, and you may not have to give em much or any feed/grain, they seem to hold weight fine for the most part. Change of feed at any time is done gradually, no sudden changes.
We try to feed them in increments so that there are no real long spans without feed, with a preference for the best grass hay that can be afforded, not easy, average is 3000 bales/year, some years the hay is poor, due to weather. Not easy keeping horses is it ? LOL !