Depended on where they were, what they did, yes, men carried sidearms. In some places in the west, it was illegal to carry arms. eg, in Mexico and some border areas, it was taken as prima facie evidence of illegal carrying of arms if you were found wearing a gun belt and holster. So the vaqueros took to carrying their SAA's just stuck into their waistbands or pants belt; this way, if someone "official looking" came riding up on them, they could toss the gun away from themselves and claim ignorance of it, not having any holster or gunbelt on them.

In reading the history of Wyoming west and down through the Great Basin, many more people had a carbine or rifle close at hand than had a handgun on their hip. Storekeeps usually had a cheap, sawn-down shotgun instead of a handgun at their disposal.

100 years ago, many men "in town" carried a handgun concealed - a SAA is a tad large for concealed carry. My grandfather carried a Colt 1903 Hammerless .32 ACP concealed on when he worked on Wall Street in the days before/after WWI. He said that lots of men carried .22 to .32 pistols in that day - there was no shortage of "ruffians" who would try to rob you on the street after dark if you turned down the wrong street in NYC in those days. A gentleman was supposed to deal with these things for himself. Lawerence Livermore, one of the most notorious of the Wall Street operators, killed himself with a 1903 Hammerless in 1935 in the mens' room of a restaurant in the business district - so it was a common practice well after the Sullivan Laws were in effect in NYC.

No, people didn't go out into the street and "shoot it out." That's an invention of Hollywood.  Hollywood gets nearly everything about guns wrong. The physics, the round count, the lethality, the use, you name it. Hollywood has their own warped version of reality.


Want to read some books on the reality of privately owned arms being used? Read up on a little incident that happened in the county south of where I am: The Johnson County  War. Here's some perspective on it:

The Texas perspective: 

https://legacy.lib.utexas.edu/taro/tamucush/00155/tamu-00155.html

The Wyoming perspective:

http://www.wyomingtalesandtrails.com/johnson.html

The political establishment penalized Johnson County for their uprising by making sure that no railroad would ever run through Johnson County. To this day, there are no rails in Johnson County. The Wyoming Stockgrowers files in Cheyenne are cleaned out around the year 1892, and Johnson County still enjoys quite a bit of Democratic voter registration in an otherwise solidly Republican state. Bumper stickers are still seen on Johnson County vehicles (you can tell these by the "16" on their license plate number) that read "Johnson County: We haven't trusted Cheyenne since 1892."