There are some basic problems with this question.

First, women didn't have the right to vote at the time. Prohibition was ratified by the final necessary state January 16, 1919. The final state to ratify the 19th amendment, which gave women the right to vote, did so on May 21, 1919. Only 15 states had given women the right to vote before this.

Also, "most of the men" were not overseas fighting in WW1 at the time. US forces numbered around 2 million. At the same time the population of the US was around 100 million.