Long ago before I revealed my true identity (!!!) I gave this answer to a similar question. I can now reset that answer in more direct terms with my identity revealed since I no longer lurk in the shadows!

This question is addressed in the saloon chapter of my Virginia City: Secrets of a Western Past (U of Nebraska, 2012). In northern climates, batwing doors would never have worked; saloons in the Intermountain West generally had full-length doors. Even in towns with twenty-four hours of shift workers, saloons would have closed in the early morning hours, and there was a need to be able to close and lock the front doors. Although Virginia City and the Comstock Mining District did operate three eight-hour shifts, primary sources including diaries and newspapers clearly indicate the saloons closed in the early-morning hours.

Another thing that Hollywood gives us is a different orientation: doors open in films on the longest wall. Saloons, in fact, were orientated to have the least front footage since that was the expensive real estate, so doors opened to long narrow saloons with the saloon leading back to the back wall. But that doesn't work fr cinema, so Hollywood turned the saloon so the doors opened to the broad bar on the opposite wall. Batwing doors were used occasionally in the Southwest, but they were always backed up with tall doors that could seal the saloon for security or against the wind (and occasionally cold winter nights).