At the 1936 Olympic Winter Games in Garmisch-Partenkirchen, Hagen earned three medals in four days. On 10 February he skied the leadoff leg for Norway's 4x10km relay team. The Norwegian team lost to the athletes from Finland by only 20m, but they were far ahead of the third-place team
Two days later, Hagen took part in the 18km cross-country race, finishing second behind Erik-August Larsson of Sweden. This race also served as the first half of the Nordic combined event. Since Larsson was only a skier, Hagen took a lead of more than two minutes into the ski jump portion of the Nordic combined. Although his score was only the sixteenth best, Hagen achieved a clear victory.