As you can see here, some members of the Audobon Society had to place themselves strategically on the trail to avoid stepping in horse manure. This does create a technical problem for the group. Watching the trees and shrubs fore birds and keeping an eye on where you are stepping, all at the same time, can be rather difficult.
"Horse manure generates so much heat as it decomposes that large piles of it have been known to spontaneously combust." - Little Book of Horse Poop by Becki Bell.
As you can see in the above quote, beside the issue of dog versus horse equal rights, is the danger of horse apples causing forest fires in our beloved parks. I rest my case. :-)