Originally selected by the Blues in the third round (86th overall) in the 2020 NHL Draft, Peterson debuted with the Thunderbirds on April 14, 2024, recording an assist in his first game against Providence.
Prior to turning pro, Peterson skated for Boston University, where he put up 60 points (23g, 34a) in four seasons. He appeared in a pair of Frozen Fours in 2023 and 2024, and he was named the MVP of the Beanpot Tournament in 2022 after scoring the game-winning goal in the Beanpot title game over Northeastern.