Some of Flint's family. The stallion has been separated from his herd.
"The bureau has forgotten that they manage our horses on our public lands," the foundation wrote on its blog.
"These aren't anonymous horses - they are well known and beloved around the world from the popular PBS Nature programmes about Cloud, one of the stallions likely to be rounded up tomorrow."
The third programme about the herd will screen in less than two months.
The foundation said the bureau was removing whole bands of horses living outside the designated range, rather than selective removal.
"This herd is just barely genetically viable at 188 horses. The bureau is reducing them to 120 - far below the minimum genetic viability levels recommended by [geneticist] Dr Gus Cothran, of Texas A&M University.
"In all our meetings the bureau told us that this would be a carefully executed SELECTIVE removal. They have since changed this to be a semi-selective removal.
"If the BLM does remove 70 horses, we want them to use the recommendations provided by experts, as they said they would in their draft and final environmental assesments as well as their herd management area plan."
The foundation said horses 20 years and older were being taken off the range.
"It costs over $US2000 to remove a horse, and no-one wants to adopt an older wild horse except to save them from slaughter and an uncertain future. Let these horses live out their lives on the range. The bureau is putting horses on welfare who don't want or require it."
The foundation said the only independent observer was being denied access. The bureau, it said, was not allowing for transparency in their handling of the wild horses.
"This is beginning to feel like a nightmare as we are being treated as powerless when it comes to protecting this herd.
"Media coverage, legal efforts, floods of calls to the White House and to the Department of Interior and the bureau and all they do is send out national bureau people to preside over this controversial roundup."