Cowboy Dictionary - Letter O
Open Cow - A cow that is not currently bred, or pregnant.
Off Billet - A strap, usually made of leather or nylon, used for securing a saddle onto a horse.
The off billet is found on the right side of the saddle. It is attached to a "D" ring on the saddle, then is attached to the front cinch. (The word "off" in off billet is referring to the right side of the horse. See the definition immediately below this one.)
Off billets have been traditionally made of leather. Today, however, off billets made of nylon are also common.
Below: The yellow arrow is pointing to an off billet.

Off Side - The right side of a horse. The left side of a horse is the "near" side.
Ox (Definition 1 of 2) - A male animal belonging to the genus Bos, which includes the species cattle, that has been castrated after reaching sexual maturity. The plural of "ox" is "oxen."
Ox (Definition 2 of 2) - Any member of the Bos genus (usually male, but can also be female) that is used for draft work.
Oxbox Stirrups - A kind of stirrup that has a rounded or "U" shaped appearance.
Below: An oxbow stirrup.

Oxbow stirrups (often simply referred to as "oxbows") are used by all types of horseback riders but are primarily seen among working cowboys and cowgirls.
Fans of oxbow stirrups like them for several reasons, including describing them as easier to "keep" (less likely to slip out of them) during hard or rough riding than other types of stirrups.
In addition, riders that prefer oxbows say that their design helps to prevent a rider's foot from hanging up when the rider is "in a storm," such as when a horse is bucking.
You can shop for oxbow stirrups here.
CowboyWay Dictionary