CAÑON CITY, Colo. — The herd of wild horses clopped cautiously toward the strangers in their pen. A chestnut mustang leaned in for a closer look, sniffing and snorting curiously. Another inched backward, her black eyes flashing with fear.

For many, this would be their first human contact, beyond the workers who feed them at this 80-acre holding center, 100 miles southwest of Denver.

“They have all their needs met here. Except their freedom,” said Fran Ackley, who oversees the Bureau of Land Management’s Wild Horse and Burro Program in Colorado. “I can’t say if they want it or not.”

Long a totem of the American frontier, the tens of thousands of wild horses who roam across forgotten stretches of the rural West are at the heart of an increasingly tense dispute over their fate. The bureau says their numbers continue to grow at an unmanageable rate, despite years of removing wild horses from the range to enclosed pastures so that wildlife and livestock can share the land.