Some groups have tried getting horses banned from trails in our state. Our group, Backcountry Horsemen of America- has lobbiests in state and federal government and so whenever a threat appears, we rally but it is kind of silly when you think of it.
The trails were built with the tools the "stock" carried up there.
My biggest complaint is hikers who leave toilet paper 2' from the trail and their own human waste but complain about a little horse poop on the trail. Seems they always complain until they get lost or injured and we do our best to save their yuppy butts.
One of the main reasons to join is to support the political causes that come up, and to promote good shared uses in the state forests. Our local politic is really pretty good in capital forest now, the motorized ORVs have their own half of the mountain and we have ours, the local groups do a lot of good PR with hikers and bicyclists and it's a very friendly environment. But that takes work, and a lot of signs up reminding everyone who helps to maintain those trails for everyone.