The life of wild mustang Cloud has been documented since his birth. His herd, from the Pryor Mountains in Montana, is being rounded up and "removed".
The foundation has condemned the muster and labelled the Bureau of Land management a "rogue government agency".
The foundation and wild horse advocates have been at odds with the bureau, taking opposing views on the genetic value of the herd and the quality of conditions in the range that the herd inhabits along the Montana-Wyoming border.
The Cloud Foundation and Front Range Equine Rescue failed this week in a bid to get a court order stopping the muster.
The bureau intends to gather the entire herd and remove 70 animals, which will be offered for adoption. The herd includes a famous palomino stallion named Cloud, whose life has been recorded by documentary maker Ginger Kathrens.
The Equine Welfare Alliance has also condemned the gather, saying the operation targeted "America's most famous wild horse herd".
The Cloud Foundation confirmed that the muster got under way on Thursday in 90-degree heat, as five mustangs were driven into corrals by helicopter.
"This unique little herd is being destroyed starting now," says Kathrens, who is volunteer executive director of the foundation.
"Seventy horses and some foals are to be removed from their spectacular home in the wild and this will leave us with a non-viable herd."
Geneticist Dr Gus Cothran, of Texas A&M University, described the roundup as overkill.
Critics say that it is clear the bureau is refusing to listen to science and the wishes of the public.
The gather is expected to take four to 10 days.
Wild horse advocates and biologists argue that the bureau is going against its own environmental assessment for the removal, and ignoring the unique genetics of this herd.
"Removing an entire subpopulation is not the way to manage a small, precious and unique population of animals," says Kathrens.
"People enjoy seeing the horses in the Custer National Forest and extensive evidence exists that these horses have been in this area for centuries.
"It is vitally important that this range be legally expanded to allow this herd to grow to safe, genetically viable numbers."
The bureau says it is necessary to remove 70 horses to "maintain a thriving natural ecological balance". However, the view is rejected by horse advocates.
"If the range was that poor than why do we have fat 20-plus year old horses who look like they are half that age?" asks Golde Wallingford, owner of a Pryor Mountain mustang.
"The bureau is feeding the American public lies and it is time for them to stop," she said.
Wallingford, who traveled to the Pryors to protest, noted that the range is still green in late August after three years of above-average rain which followed a long drought.
"Why are they removing nearly half the horses after the drought is over?" asks Howard Boggess, a Crow elder and historian. "Everything that is against the law for me they are planning to do to these horses."
The Cloud Foundation's Kathrens says: "We are losing our wild horses on our public lands as a rogue government agency is left unchecked.
"Our government has promised it will listen to us. The public is crying out for these wild horses and their voices are getting louder. We need our new administration to start listening or our American mustangs will go the way of the buffalo."