Schremp grew up in Fulton, New York. As a youth, he played in the 1999 and 2000 Quebec International Pee-Wee Hockey Tournaments with a minor ice hockey team from Rochester, New York. He decided a move to Canada would benefit his hockey career and he spent his major junior years in the Ontario Hockey League (OHL). He spent his rookie season with the Mississauga IceDogs and after recording 26 goals and 74 points in 65 games, was named OHL rookie of the year for 2002–03.