A days-old filly foal in the Pryor Mountains. She is a member of Cloud's herd and is to be rounded up by federal authorities.
The Cloud Foundation and Front Range Equine Rescue had sought a temporary restraining order against the Bureau of Land Management to stop the muster of the herd, which had been scheduled to begin on Monday.
The muster was delayed pending the outcome of the hearing. On Wednesday, US District Court Judge Emmett Sullivan delivered an oral ruling rejecting the application for the order.
The Cloud Foundation said the muster was to begin on Thursday (today, New Zealand time).
The bureau intends pulling all 190 wild horses from the 38,000-acre wild horse range in the Pryor Mountains, which run along the Montana-Wyoming border. The herd includes a stallion called Cloud, whose life has been recorded by documentary maker Ginger Kathrens.
It intends releasing 120 of them back into the wild, but after giving mares a long-term contraceptive injection. The other 70 will be offered for adoption.
The groups challenging the muster claim the plan could end up destroying the viability of one of most genetically pure herds of Spanish colonial horses in the United States.
They point to the opinion of geneticist Gus Cothran. of Texas A&M University, who said 150 to 200 animals are required to maintain genetic viability.
The Pryor Mountain wild horse range was created in 1968 and has been culled on three previous occasions - in 1997, 2001 and 2003.
The Equine Welfare Alliance described the planned Pryor Mountain operation as an action unprecedented in size and scope. It said the operation targeted "America's most famous wild horse herd".
A series of other concerns have been raised over the muster, which are outlined on the Cloud Foundation website.
The use of helicopters in the roundup has also been condemned.
Kathrens, who is volunteer executive director of the Cloud Foundation, said: "Fully knowing the public's concern about wild horse roundups, the bureau is still debating whether independent humane observers will be granted access to round up operations in the Pryors.
"Where is the transparency and full-disclosure of this new administration?"
Kathrens says young foals, only days old, will be rounded up and potentially removed.
The bureau's website explains that the roundup is necessary "to achieve a thriving natural ecological balance on the Pryor Mountain Wild Horse Range".
It argues the range does not have the capacity to sustain the current wild horse population over the long-term on healthy rangelands.
"Several studies over the past few years show that parts of the range are in very poor condition. These range studies were comprehensive and quantified. The higher and lower elevations of the range are suffering resource damage.
"Use of the middle part of the range is limited due to few water sources. The BLM is prohibited from allowing a 'deterioration of the range associated with an over-population'[of wild horses]."
It planned to remove about 20 males and 50 females from the range.
It said genetic testing done between 1991-2001 showed that the "current levels of genetic diversity within the Pryor Mountain herd are relatively high for a wild horse population, are well above the mean for domestic breeds, and have been steady during the period of the studies".