Actually, you need to contact the Lander BLM office. The Green Mountain area actually lies in their administrative area.
Hopefully they're looking at gathering horses after the hunting seasons, but they're probably limited by the availability of a gather crew and chopper. The horse advocates (basically animal rights groups) pushed through rules that don't allow for gathers during much of the year because of supposed stress to the horses and possible impacts to foals during the spring and summer. Sometimes the short-term detriments of conducting a gather and impacting public lands users is outweighed by the benefits of keeping the horse populations at proper levels.
As far as I know, the gathers use helicopters and riders on horseback, they don't run them with four-wheelers. I doubt that the impacts of the gather will be any worse than all of the idiot "sportsmen" that will run all over the area, both on and off-road in their ATVs and pickups...I'm speaking from past experience.