MUNICH—Half a century ago, a German sculptor’s widow and an elite Bavarian boarding school agreed on a novel way to cover her son’s tuition: She donated a bronze horse that her husband had made for Adolf Hitler.

The 10-foot-tall horse still stands in the school’s courtyard, unremarked until early this month, when a Munich newspaper wrote about it. The revelation has sparked a battle between the Schloss Ising boarding school and local…