Half Siblings
Horses out of the same dam but by different sires. Horses with the same sire and different dams are not considered half-siblings in Thoroughbred racing.  

Halter
Like a bridle, but lacking a bit. Used in handling horses around the stable and when they are not being ridden.  

Hand
Four inches. A horse's height is measured in hands and inches from the top of the shoulder (withers) to the ground, e.g., 15.2 hands is 15 hands, 2 inches. Thoroughbreds typically range from 15 to 17 hands.  

Hand Ride
Urging a horse with the hands and not using the whip.  

Handicap
1) Race for which the track handicapper assigns the weights to be carried. 2) To make selections on the basis of past performances.  

Handily
1) Working in the morning with maximum effort. Compare with, 2) A horse racing well within itself, with little exertion from the driver. 

Handle
Amount of money wagered in the parimutuels on a race, a program, during a meeting or for a year.  

Harrow
Implement or unit with pulling teeth or tines used to rake and loosen the upper surface of a track.  

Head
A margin between horses. One horse leading another by the length of its head.  

Head of the Stretch
Beginning of the straight run to the finish line.  

Helmet
A lightweight fiberglass cap worn by drivers to prevent head injuries. It is required equipment. 

Homebred
A horse bred by its owner.  

Horse
When reference is made to sex, a "horse" is an ungelded male five-years-old or older.  

Hung
A horse that does not advance its position in a race when called upon by its driver is said to have hung.