Meet Thomas E. Dewey, the last major US presidential candidate with facial hair. He ran in 1948.
It was over a quarter of a century before either major party chose a candidate with facial hair. But faced with the hopeless task of displacing Franklin Roosevelt in 1944, the Republicans opted for the moustached Thomas E. Dewey. He was chosen again to oppose Harry Truman in 1948, and while he did better than two cleanshaven minor candidates, Henry Wallace and Strom Thurmond, he was defeated by Truman. All serious presidential candidates since have been cleanshaven.
A neat analysis of facial hair and US presidential elections: Link