Issue a news release about overpopulation and excess animals.
Say nothing about forage allocations and the prevalence of livestock.
Float the idea of motorized removal.
They’ll be begging for nonmotorized removal, with ovary-killing pesticides, and they’ll provide it themselves at no cost to the government.
Western Horse Watchers Association 
Sorry, but unsure of who is represented by the lovely ladies [?!] in the picture, and exactly their goals and motives. The picture alone suggests population control should be expanded to species beyond equine-ish. wolfish, and porcine.