Amigo – Friend.
Bronc – An untrained horse.
Bronco Busting – “Breaking” (tanning) horses so that they could be trained and ridden.
Broomtail – A range horse with a straggly tail.
Calaboose – Jail.
Cayuse – A small horse, especially an Indian pony.
Chaparral – Dense thicket of thorny bush.
Chaps – Abbreviation for chaperejos, meaning leather leggings.
Chuck Wagon – A wagon adapted for use as a portable cooking stove and place to store food.
Cinch – A wide strap to hold the saddle on a horse.
Corral – Fenced yard for animals.
Cutting Out – Separating a calf and its mother from the herd so that it could be branded.
Drover – A professional who was responsible for organizing, planning and leading a trail drive.
Horn (Pommel) – The post on the front of a Western saddle. Cowboys tied their lariats to them when dragging firewood or pulling cattle.
Lariat – A long rope, often looped so that cowboys could “lasso” (make a slipknot and capture) cattle.
Lasso – A rope with a running noose.
Line Camp – An isolated camp used as a base when patrolling distant parts of a large ranch.
Outlaw – A horse that cannot be broken.
Pinto – A spotted horse.
Quarter Horse – A small animal that can run quickly for short distances. It is descended from a breed trained to run quarter-mile races in the East.
Remuda – The herd of horses from which cowboys chose their mounts. It comes from the Spanish word for “replacement,” since cowboys used several horses a day to keep from overtiring animals.
Rodeo – Cattle roundup, or a demonstration of cowboys’ skills.
Sorrel – A reddish-brown horse.
Stampede – A sudden scattering of cattle or horses.
Sun Fisher – A bucking bronc.
Tally Man – A cowboy who kept track during a roundup of what cattle belonged to which ranch.
Tapadero – A leather hood on the stirrup designed to protect the boot.
Vaqueros – Early Mexican cowboys, who lent the North American cowboys many of their customs.
There are many more cowboy phrases, but these should give you a start.