In 1967 Cowan graduated from Dartmouth College and served in the Peace Corps in Dessie, Ethiopia (1967–1969).
While in Ethiopia, he taught English at Woizero Siheen High School and became fluent in Amharic.
Cowan moved to Louisville and worked for the campaign of Harvey Sloane for Governor of Kentucky in 1978–1979.
In 1987 he ran for Attorney General of Kentucky and defeated Todd Hollenbach in the Democratic primary.
As Attorney General he successfully argued Stanford v. Kentucky before the United States Supreme Court in 1989.