Holzmann was born in Bad Wörishofen and grew up in Memmingen . When he was at primary school, he moved with his family to Oberstdorf , where he still lives today. He competed in his first races when he was six. At the age of 15 he started in FIS races in January 2010 . A specialization in slalom and giant slalom became apparent early on. His first victory in an FIS slalom was in February 2012 on the Feldberg . He made his debut in the European Cup in January 2013, and made it into the points for the first time in December 2013. In the same year he became German giant slalom champion.
On January 6, 2014, Holzmann was in action for the first time in a World Cup race and reached 54th place in the slalom in Bormio . At the 2014 Junior World Championship in Roccaraso , he won the bronze medal in the team competition . In contrast, the next two seasons did not show any significant progress. The first World Cup points were not won until January 5th, 2017 when he finished 19th in the Zagreb slalom . In March 2017 he took part in several races of the Far East Cup ; with three wins and one more podium place, he finished second in the slalom classification and third in the overall classification.
Holzmann achieved his first podium in a European Cup race on January 26, 2018 with second place in the Chamonix slalom . His best World Cup result so far is an eleventh place, which he achieved on March 4, 2018 in the Kranjska Gora slalom . In the 2019/20 European Cup , he won the slalom classification, including his first victory in a European Cup race (on January 21, 2020 in Jaun ).