"We've got permission to use the cannon!" says Ismar Biogradlic, the coach of Bosnia and Herzegovina’s national snowboard team, with a smile. “Hurry up!”

A snowcat waits for us, orange lights flashing in the dusk. We hoist a coiled length of hose onto the flatbed and climb up. Biogradlic, a 37-year-old man with close-cropped graying hair and a ring in his left ear, taps the roof of the cab and yells “Go!” The driver revs the engine, and the cat jerks forward like a tank.

After hours of negotiations, Biogradlic has finally convinced the state officials who own Bjelasnica, a ski resort near Sarajevo and a former Olympic venue, to let him use a snow gun. It’s early February, normally the snow­iest month in Bosnia’s Dinaric Alps, but Bjelasnica’s trails are barely covered and­ ­entirely devoid of skiers. This is problematic for Biogradlic. In less than a week, he is scheduled to host a slopestyle and big-air event for the Snowboard Europa Cup—a small-budget Euro­pean version of the X Games—at the ­resort. But Bjelasnica’s management, a couple of decades and one significant war removed from the salad days of the 1984 Sarajevo Olympics, is pinching pennies, and Biogradlic has only a few hours with the snow gun.

As we grind up the hill, the snowcat churns up a stew of gravel and dirt. High on the peak, the skeletal remains of rusted-out chairlift towers that haven’t operated in 20 years are silhouetted against the evening sky. Around us, in the surrounding forests, red signs issue a harsh warning: MINES! KEEP OFF!

At the top of the terrain park, we jump off the snowcat. “Quickly,” Biogradlic says, shoving a pickax into my hands. “Start digging a trench."

The snow gun, brought up by another cat, is set strategically over the slope. While I dig a protective trench for the hose and cables running between the hydrant and the gun, Bio­gradlic makes sure the connections are tight. Enes Vilic, 26, one of Bosnia’s best freeskier...