CHEYENNE, Wyo. (AP) — If you ever wished to gaze at a stomping, snorting, neighing panorama of Western heritage from your living-room window, now could be your chance.

A classic image of the American West — wild horses stampeding across the landscape — not only has endured through the years but has multiplied past the point of range damage. Through May 3, the U.S. government is seeking more private pastures for an overpopulation of wild horses.

Many consider rounding up wild horses to live out their lives on private pastures a reasonable approach to a tricky problem. Wild horses, after all, no...