The Pryor Mountain herd includes a wild stallion made famous by a documentary maker.
Cloud is a pale palomino whose life has been documented from the day of his birth by Emmy-winning filmmaker Ginger Kathrens.
The Bureau of Land Management intends taking all 190 wild horses out of the mountains, on the Montana-Wyoming border, and reducing their number to 70 before releasing them back.
The Cloud Foundation and Front Range Equine Rescue have sought an injunction in the Federal Court in Washington, DC to prohibit the bureau from removing the horses.
They argue that reducing the herd to 70 horses will leave it below genetically viable levels and unable to sustain itself.
Equine geneticist Gus Cothran has said 150 to 200 horses would be required to achieve the minimum effective population size.
The Pryor Mountain muster is part of a bureau plan to round up nearly 1000 wild horses from the western rangelands in coming weeks to bring herd numbers into line with its own recommended management levels.
The operations will involve the use of helicopters and ground-based musterers to herd the horses.
Some of the captured mares will be released after being given long-acting fertility treatments.