The conclusion of Snuggerud's decorated career at the University of Minnesota led to the beginning of his professional career when he signed his entry-level contract with the St. Louis Blues on March 28, 2025. Among the highlights of a solid rookie season with the Blues were his first three-point game in the NHL (one goal, two assists) in a 4-3 overtime loss to the New York Islanders on March 10, 2026, and six points (three goals, three assists) in four games to earn the NHL Third Star for the week ending March 15. He was then named the NHL Rookie of the Month for March after becoming the first Blues rookie with at least 15 points in a calendar month since Rod Brind'Amour had 15 in November 1989.

The forward and top 10 finalist for the 2025 Hobey Baker Award was chosen in the first round (No. 23) of the 2022 NHL Draft. He was named Gophers captain for his junior season and led them with 24 goals, 27 assists and 51 points in 40 games while earning Big Ten First Team All-Star honors for the second consecutive season. Snuggerud finished his tenure at Minnesota as one of only three players in program history to score at least 20 goals in three consecutive seasons to begin his collegiate career.

Snuggerud, a native of Minneapolis, played for the United States at the 2023 and 2024 IIHF World Junior Championship, the latter when he helped his country win a gold medal. He is the son of retired forward Dave Snuggerud, who played 265 games for the Buffalo Sabres, San Jose Sharks and Philadelphia Flyers, and a third-generation player at the U., joining Dave (1986-87, 1989) and his maternal grandfather, James Westby (1958, 1962-63).