In January 1994 Hornschuh made his debut in the Ski Jumping World Cup in Liberec by jumping on the normal hill and was the 25th to win the first World Cup points. From now on, the Thuringian was generally part of Germany's World Cup team, but was mostly overshadowed by more successful jumpers. His performance often fluctuated between reaching and missing the second round. Placements in the top twenty occurred again and again, but remained the exception. It wasn't until 1998 in Zakopane that he came close to the best for the first time in eleventh place. Two months later, he finished eighth in Oslo , his first single-digit placement. At the start of the 1998/99 season , Hornschuh achieved further top ten results in Lillehammer with ranks seven and nine. It should be the start of his best World Cup season, which peaked in December in Harrachov with a second place behind Janne Ahonen . In the overall standings for the season, Hornschuh took 26th place. After the season, the German's performance deteriorated, and new jumpers pushed into the German team. He played his last jumping in 2000 as part of the Four Hills Tournament 2000/01 in Oberstdorf , but was 49th and failed to qualify for the finals.
Hornschuh competed 76 times in World Cup ski jumping. Four times he was among the top ten, 31 times he reached the finals and won points. He never took part in the World Championships or the Olympic Winter Games because of stronger German athletes. From 2010 to 2015 he worked as the head ski jumping base trainer of the German Ski Association in Thuringia and has been the national trainer for Switzerland since 2015.