This was a potential problem. In Virginia City, Nevada, during the heyday of the Comstock Mining District (1860-1880) teamsters had to deal with the steep slopes of the community. Primary sources speak to numerous runaway wagons. The animals were secured to the structure of the wagon, of course, so if they could not keep up with the speed to the runaway, they would veer to the side and the wagon to tip over with its contents sprawling downhill - and there was potential injury to the animals.
Teamsters would ride the brakes on downhill trips to keep the wagon from getting away from the team, but this was risky business with heavy loads - particularly when hauling tons of ore downhill to the mills.