No, because first of all hay is not an organism.
example of mutualism
horse=livestock+hay
No. A horse is a heterotroph, it feeds off producers - ie plants.
No, horse feces does not turn into hay. Horse feces is composted and it turns into horse manure. This is used as a fertilizer.
Any hay can founder a horse, it is not what the horse eats but how much it eats. Some feed can founder a horse faster than others. Peanut hay is one of those.
Hay!
Hay-Burner
Are you asking is it okay to ride a horse when they are on just hay? It is completely fine to ride a horse that is on just hay. My horse is fat as a cow and she was on all hay, no feed all summer. I rode her regularly.
A monkey
No second cut hay often has more nutrients in it than first cut hay. But if the horse is overweight or not working much then first cut hay would be better if the horse will eat it.
A hay check.
human body