If the cowboy had a rope or handmade lariat
it probably would be on the right side of the
saddle.
Regarding the saddle, note the
minimal trappings, a lightweight rig compared
to so many saddles today and no saddle
blanket is apparent.
In the cattle driving days, remudas were large
and cowboys could during a workday wear out
a lot of horses, the animals getting very tired
and in need of rest.
I believe the cavalry of the late 19th century
set a maximum weight for its troopers of around
160 pounds or less. The rider plus the saddle
and equipment was meant to be kept at a
maximum of just slightly over 200 pounds, all
in the name of saving the horses.