Uh Lee
There is one little problem with your analogy: The differing lengths of the periods of time involved. You remember how FDR was in at the beginning of World War II? You remember how he led the country through about 95% of it before expiring just short of the finish line?
Now, Reagan was around at the dawn of the Cold War, 'tis true. As a distinctly B-list Hollywood actor, transitioning into a second career as spokesmodel for GE. But I think it's fair to say he had little hands-on involvement until taking office in 1981, wouldn't you agree?
The Cold War was a multigenerational project executed by a relay race of nine Presidents who handed the baton off to the next guy.
Reagan was the eighth runner.
Bush brought it across the finish line.