This is likely the bearing rein, used in horse carriages. The
bearing rein was used to force the horses head into an upright
carriage to make it look more stylish. However it had bad physical
side effects on the horses, including pinched nerves, muscle pain,
back problems and breathing trouble. There are other devices that
can be used while the horse is being ridden that work similarly to
the bearing rein, these include the De Gogue among others.