At the age of three, Holzmann was on alpine skis, until she was seven years old she did cross-country and alpine skiing. After that, she concentrated only on alpine sports and was active for the Oberallgäu regional team, allgäu ski association (ASV) until the 2009/10 season. Because of multiple patellar luxations , she had to end her career in alpine sports. She came to telemark sport through her parents and brother Benedikt Holzmann , so she stood on telemark skis for the first time at the International German Telemark Championships in 2010 and became German youth champion in the classic sprint. In autumn 2010 she joined the German telemarketing team. On January 12, 2011 she made her debut in the Telemark World Cup in Bad Hindelang / Oberjoch . At the World Cup stations in Bad Hindelang and Rauris, she achieved good results with places 12 and 13. In the further course of the season she was able to consolidate and improve her good results. In the overall ranking and in the Classic she came in 11th place. Tenth place in the Classic and 13th place in the giant slalom. At her first Junior World Championship in Hafjell in 2011 , she won the silver medal in giant slalom, classic sprint, classic and overall (giant slalom, classic sprint, classic). At the International German Telemark Championships 2011 she won the silver medal in the Classic Sprint. In the first half of the 2012 season , she was able to build on her good results from the previous year, so at the World Cup in Kvittfjell she came third in the Classic and Classic Sprint. A few days later she was second in the parallel sprint at the World Cup in Rjukan . In the legal World Cup stations, it was never worse than fifth, so it finished fifth in the overall World Cup. In the Classic, Classic Sprint and the parallel sprint she came in sixth place. At her second Junior World Championships in Espot in 2012 , she won the gold medal in the Classic, Classic Sprint and Parallel Sprint. She won her second gold medal at the International German Telemark Championships in 2012. In the 2013 season , she could build on her good performance of the year. Because she won Vallée de Chamonix third place in the Classic race. In the overall World Cup and in the discipline classification she reached fifth place. In her third participation in the Junior World Championship in 2013 , she won the gold medal in the Classic and Classic Sprint. At her first World Championship in 2013 in Espot, Spain, she achieved fifth place in the Classic, Parallel Sprint and seventh place in Classic Sprint. She won the silver medal in her fourth participation in the International German Telemark Championships in 2013.
In the 2013/14 season she made it onto the podium four times and otherwise among the top ten. At the end of the season she finished sixth in the overall World Cup ranking, fifth in the Classic, 11th in the Classic Sprint and eighth in the parallel sprint. In her fourth participation in the 2014 Junior World Championship in Geilo , she won the gold medal in the Classic and Classic Sprint. At the telemark championships she won the silver medal for the third time. At the beginning of the 2014/15 season , she finished second in both the Classic Sprint and the Parallel Sprint races in Hintertux. In the further course of the season she achieved five podium places and in Rauris Holzmann was disqualified in the Classic Sprint race. In the overall World Cup ranking she came in third place, in the classic in fourth place, in the Classic Sprint in fifth place and in the parallel sprint also in third place. At the Junior World Championship 2015 in Steamboat Springs she won the gold medal in the Classic and Classic Sprint and fifth in the parallel sprint. At the 2015 World Championships, which was also held in Steamboat Springs, she came fifth in the Classic Sprint, fourth in the Parallel Sprint and did not start in the Classic.