Cordin got into skiing at an early age through his father, who was successful in Nordic skiing in the 1930s. After he moved to St. Anton am Arlberg with his family, he became a member of the Arlberg Ski Club . At the beginning of his career he achieved the best results in the technical disciplines of slalom and giant slalom . In 1967 he was on the podium for the first time in an FIS race in the slalom at Puerto de Navacerrada . But the downhill soon became his specialty.
Cordin achieved his breakthrough in the World Cup in January 1969 with two third places on the Lauberhorn in Wengen and on the Hahnenkamm in Kitzbühel . With two more top 5 results, he achieved sixth place in the Downhill World Cup in the 1968/69 season . In addition, he became Austrian downhill champion for the first time in 1969 . In the winter of 1969/70 Cordin first came second in Wengen and also second in Garmisch-Partenkirchen . At the 1970 World Cup in Val Gardena , he won the silver medal behind the Swiss surprise winner Bernhard Russi . A week after the World Cup, he celebrated his first World Cup victory in the last World Cup downhill this winter in Jackson Hole , with which he won the Downhill World Cup tied with his compatriot Karl Schranz .
In December 1970, Cordin scored his second victory in a World Cup descent in Val-d'Isère . After further top 10 results, the next podium followed at the end of the 1970/71 season and thus third place in the Downhill World Cup. In 1971 he was also Austrian downhill champion for the second time. The 1971/72 season was less successful , in which he achieved five top 10 results but no podium and fell back to eleventh place in the Downhill World Cup. At the 1972 Winter Olympics in Sapporo , Cordin was seventh. In the winter of 1972/73 he achieved a podium again with second place in Val Gardena and he improved to sixth in the Downhill World Cup. On December 18, 1973, Cordin celebrated his third and final World Cup victory in Zell am See , making him sixth in the Downhill World Cup this winter. At the 1974 World Cup in St. Moritz , he was fourth and missed the bronze medal by less than a tenth of a second.
In the 1974/75 season , Cordin was affected by a meniscus injury that he suffered in training. His best result of the season was fourth place in St. Moritz. In another four World Cup descents he was among the top ten, in the Downhill World Cup he fell back to eleventh place. At the beginning of next winter he got two top 10 placings, but after his knee problems got worse, he announced his resignation in January 1976 for health reasons. Cordin later became a successful tennis player . In the 1990s, he was multiple ski tennis world champion in his age group.