Cozens served as an alternate captain for Team Canada at the 2019 IIHF World U18 Championships. Cozens won Gold with Team Canada at the 2020 World Junior Ice Hockey Championships, scoring once in their 4–3 win over Russia. He and Bowen Byram were named co-captains for Team Canada at the 2021 World Junior Ice Hockey Championships on December 26, 2020, replacing injured captain Kirby Dach. After going undefeated through the tournament, Cozens and Canada lost in the Gold medal game to Team USA 2–0.