The truth of the matter is that most 'cowboys' didn't carry when plying their trade - that of herding cattle.
Most of the revolvers were kept in their gear, on the wagon.
Range bosses didn't like that their hands were often 'excitable' young men and prone to fighting - and when given weapons - were more than ready to use them - so, they kept them away from the hands unless actually needed because of a threat.
As an aside, the 'John Ford Reference Library' is a poor way to research the times - as are the studio photos that are full of photographer's props - and the atmosphere of C&WAS does little to foster actual research into the era, when movie lore and Dime Novel excitement beckons - I mean, who needs 'real life', when 'reel life' will do?
Besides, if C&WAS replicated the times - everyone'd be dipped in a barrel of alkali dust and made to squint into the sun for hours and hours - wiping dust and swatting flies.
Another thing - the cowboy wasn't paid much - and once he'd bought a badly-needed new shirt and trousers after the drive - and maybe a new pair of boots - there just wasn't much left with which to buy extra firepower, when what he already owned was still working.
His priorities were in clothing himself and making sure his primary piece of gear - his saddle - was in good order - 'not' in wandering the town - which likely had a 'No Guns' rule - all dolled up like Billy Badass.
These were small men - boys, really - and when you're topping out at 'maybe' 5'5" - two revolvers are a lot of weight to carry.
Both the 'Historical Society' forum and the 'NCOWS' forums are filled with good, solid references in their 'back pages' - so take some time, and look 'em over.
Vaya,
Scouts Out!