Scenes from the wild horse roundup in the Pryor Mountain area.
"However, we have not yet made substantial progress and until the courts rule we need to keep Conquistador, Shane, Bo and Trigger's bands intact," the foundation wrote on its blog, which provides ongoing updates of the Bureau of Land Management gather.
The entire herd, comprising 188 animals, is being pulled from the range, with plans for the release back into the wilderness of 120 of the animals. The remaining 70 will be offered for adoption.
"These horses represent an entire sub-population of the Pryor herd, unique genetic lines that will be lost forever when they are removed," the foundation says.
"We want them to stay together and we have several options lined up, but will need financial backing. It is our intention to keep these horses close to their mountain.
"We need to fundraise for these bands and for our continued legal action to preserve this herd as well. We want to see their range expanded so that the Custer National Forest lands, where Pryor Horses have lived for at least 200 years, will be legally their's forever."
The bureau and the Cloud Foundation have been at odds in the lead-up to the gather, which began last week, over the ability of the range to support the herd and the genetic value of the animals' bloodlines.
The foundation says calls to the government and bureau have not been working, with no concessions made.
The foundation described the muster of the most famous horse in the herd, a stallion named Cloud, whose life has been recorded by documentary maker Ginger Kathrens.
"Cloud came in reluctantly and then turned and FACED the helicopter," the foundation wrote, "even taking steps back towards the range. Demonstrating his unbelievable courage and clear understanding of the trap he was about to lead his family into."
The foundation said the 19-year-old stallion Conquistador should have never been rounded-up, freeze-branded and "put through this ordeal".
"He and his entire family band are to be put up for adoption. We are requesting that the bureau turn him back out with his 10-year-old mare, Cavelitta. The whole family was removed because they live outside the designated horse range boundaries."
People for the Ethical Treatment of Animals (Peta) has offered its support,urging supporters to place immediate calls to officials. "Tell them that wild-horse roundups are inherently cruel and simply can't be carried out humanely. Demand that the bureau horse roundups, including the [Pryor Mountain roundup] be immediately cancelled."