âNo temperance in itâ¦â: Woodrow Wilson & Prohibition Because Prohibition began in Wilsonâs administration it is often assumed that he supported it. In fact, Wilson vetoed the infamous Volstead Act which enforced Prohibition and he opposed a federal law enforcing what he thought was a personal moral issue.he 1916 election was a watershed moment for the prohibition campaign. Both Democratic incumbent Woodrow Wilson and Republican candidate Charles Evans Hughes ignored the Prohibition issue, as did both party's political platforms.