Peterson was born in Winnipeg, Manitoba, Canada and began drumming at the age of three. He was a founding member of the Canadian rock band, The Guess Who, in the mid-1960s. He played with the group through to its breakup in 1975. He has participated in every reunion involving principal band members Randy Bachman and Burton Cummings, and has also joined a version of the band led by bassist Jim Kale, first in 1977, and again since 1987. He has played with the band longer than any other member and currently resides in Greensboro, North Carolina.