Dawson was educated in St. Boniface, and worked as a small businessman (owning Dawson Dry Cleaners Ltd.). He was a councillor in the Town of Rivers from 1957 to 1965, and served in the Canadian Air Force from 1957 to 1966. In 1966-67, he served as vice-president of the Canadian Amateur Hockey Association.
He was elected to the Manitoba legislature in the 1966 provincial election, defeating incumbent Progressive Conservative Barry Strickland by 151 votes in the riding of Hamiota. He lost his seat in the 1969 election in the redistributed riding of Virden, falling to Progressive Conservative Morris McGregor by 590 votes. The Liberals lost much of their rural support base in this election. Dawson did not seek a return to the legislature after this time.
He worked in the Hockey Canada organization after his defeat, becoming a life member.