Holzer belonged to the sports group of the Carabinieri . In 1987 and 1989 he was sixth in giant slalom at the junior world championships, appearances in the World Cup followed from 1990. He won World Cup points for the first time on March 1, 1991 as fifth in the giant slalom in Lillehammer . Two weeks later, the first podium followed in the Super-G in Lake Louise . On January 12, 1992 he was able to win the Super-G on the Kandahar route in Garmisch-Partenkirchen .
Due to injuries, Holzer was unable to confirm these achievements in the following years. In 1993 and 1994 he could not even classify himself in the points and was therefore mainly used in the European Cup . It wasn't until the 1996/97 season that the situation improved and he was able to reach the top of the world again. On January 5, 1999, he won the World Cup giant slalom in Kranjska Gora . After another very mixed performance, he announced his resignation at the end of the 2002/03 season.
Holzer took part in an Olympic race three times, but was never able to classify. His best result at world championships is a sixth place in giant slalom, achieved in Vail in 1999 .