All the more reason for them to object to ebike use on trails. Or bike use on trails. Many, many, many horse riders are quite wealthy and of the opinion, as wealthy people tend to be, that their right supersede other people who are less rich. If the horse groups are part of the conservation groups noted below, with their money and histories, i would not say that bodes well for adding ebikes to non motorized trails.
Frankly horses on trails terrify me. They are huge masses of easily spooked, death dealing hoofed, animals. When I am on trail and see horses I tend to put my bike behind me and back away to the edge of the trail or off the trail because I have seen horses spooked just by the sight of bike and don't want to be responsible for someone dying because my bike or my riding spooked their horse, or nor do I want to be the dead person because I ran into one on the trail because I was going faster than prudent on a multi use trail or just bad luck. I am sure they feel the same way.
I ran into many horses in Arizona, where our mountain bike trails abutted rich ranches (including spas with horses, the kinda place that Oprah and Madonna, etc visited), and we were always, as a group, very conscious of avoiding spooking or impacting the horse riders in anyway as these trails were awesome and the shear might if the wealth associated with the horse riders would be enough to easily get us shut out of these trails. Respect those with the wealth for they can change things you can only imagine.