Cosman was a native of Brockport in Western New York; he graduated from Father Ryan High School in Nashville and attended Middle Tennessee State University, signing with the Cardinals in 1963.

In 1966, after completing his fourth year in the Redbird farm system, he was a late-season call-up and, in his MLB debut on the season's last day, threw a complete game, two-hit shutout against the Cubs at Busch Memorial Stadium; the only safeties he surrendered were singles to Ron Santo in the second inning and Glenn Beckert in the ninth.

[3] Cosman divided the 1967 campaign between the National League pennant-winning Cardinals and Triple-A, working in ten games pitched (with five starts) for St. Louis.

But Cosman returned to the minor leagues for all of 1968 and 1969; he spent the latter year in the New York Mets' and Cincinnati Reds' organizations, and then was selected in the 1969 Rule 5 draft by the Cubs, for whom he made one appearance in 1970 as a relief pitcher.

In his 12 big-league games pitched (with six starting assignments), he won each of his two decisions and posted a 3.05 earned run average.