The "hay and water" mythology is a PR ploy by equestrian groups. It gets repeated over and over in different versions until most people believe it. I've been told numerous times that horses are vegetarian and their poop is organic so it's OK if it gets tracked all over my carpets. Well, 'Bent is vegetarian and his poop is organic but I don't think anyone wants it on their living room floor!
It takes some diligent googling to find science since there is so much "fake news" about horse poop. My comment that Cristina referred to was:
"Although it is true that horse feces are less harmful than dog feces, it is a myth that they are always harmless. A couple of examples: manure can carry diseases like salmonella that are transmissible to humans. If horses have taken de-worming medication, their manure can be severely toxic to dogs who sample it.
A 2012 University of Guelph study found e. Coli in 77% of manure samples from healthy horses, and over the course of a year, they found C. Difficile in manure samples from 40% of the horses in their study. It is not unreasonable for a bike rider to prefer not to get this stuff sprayed onto the mouthpiece of their water bottle. (Which has happened to me many times.)"
For those who aren't from around here, the University of Guelph is one of the most respected veterinary schools in the country, and this study was done by Equine Guelph so they like horses.