This quotation is frequently but mistakenly attributed to Churchill. It is anyway unlikely that Churchill would subscribe to this philosophy: He was a swashbuckling soldier at 20, and a Conservative member of Parliament at 25. A couple of years later he switched to the Liberal Party (which was not liberal in the modern sense), and later went back to the Conservatives.
The phrase originated with Francois Guisot (1787-1874): "Not to be a republican at twenty is proof of want of heart; to be one at thirty is proof of want of head." It was revived by French Premier Georges Clemenceau (1841-1929): "Not to be a socialist at twenty is proof of want of heart; to be one at thirty is proof of want of head