BEAVER COUNTY, Utah — When he was a boy on a 150,000-acre ranch here in the desert mountains, which are so remote that there is no power line and electricity comes from a turbine in a mountain spring, Mark Wintch would thrill at the sight of a rare band of wild horses kicking up dust as they disappeared over a rise.

“Now there’re so darned many,” Mr. Wintch, 38, said, shaking his head as he bounced his red pickup through sage-dotted public land that his family has ranched since 1935. “Look out there. You barely see a blade of grass.”

Management plans by the federal government call for no horses in this area. But five horses looked up in alarm at his truck, then wheeled off through the brush. “I counted 60 last night,” Mr. Wintch said. “If I put my cows out here, they’d starve.”

Wild horses may be a symbol of America’s unbound freedom in the Old West. But in the new West, they are a tightly controlled legal entity, protected by federal law and managed by a perplexing system on the brink of a crisis.