Paddock:  A small enclosure, usually less than an acre in size.

Palfrey:  A saddle horse for the road or for state occasions, as distinguished from a war horse (both being more common in the Middle Ages than in modern times, the latter often, though not always, called a charger).

Palomino:  A color breed whose coat is the color of a newly minted gold coin.  The mane and tail should be platinum.

Pass or transversal:  In dressage, the horse trots at an oblique forward line, head bent slightly in direction of movement.

Passage:  In dressage, a highly elevated trot, evenly cadenced, with brief hesitation of the feet at upper point of lift.

Pastern:  The short, inclined part of the foot between the fetlock and the coffin joint (hoof).  So-called because of the horse being tethered by this part of the foot while at pasture.

Pedigree:  Family tree, line of descent.

Piaffe:  In dressage, a trot in place, without moving forward.

Pinks:  In hunting, scarlet coats worn by many hunt members, called "pinks" after a London tailor of that name.

Pirouette:  In dressage, the feet moving usually in a canter, horse moves forequarters in a circle while hind feet continue in motion at center of the circle, hitting same place on the ground.

Platinum:  A precious metal that is almost white in color (used in reference to Palomino).

Point-to-point:  Amateur jumping races.  They used to be run from one church steeple (point) to the next.

Points:  Outstanding, positive features in the structure of the horse, which may compensate for minor defects.  (I believe this term can also be used to describe conformation, as in "the points of the horse," as well as color, as in "a bay with black points."  The former refers to different parts of the horse, as in the nose, withers, hocks, etc., while the latter refers to the darker colored parts on certain horses--muzzle, tips of the ears, and lower legs.)

Poll:  The summit, or most posterior part, of the head, connecting the head and the neck.  From the Middle Dutch pol, meaning head.

Pony:  All horse breeds and strains measuring less than 14.2 hands (according to at least one source, 13 hands or less) in height at the withers.  (It may be worth noting here that ponies are not really proportioned the same as horses, but that is too in depth a discussion for this particular space.)

Pony trekking:  Riding ponies over a long distance.

Post:  The action of rising and sitting in the saddle while your mount is trotting.  The reason for posting during the trot is to reduce the jarring that occurs.

Prepotency:  Quality of a sire whose characteristics appear consistently and to a marked degree in his offspring.

Produce:  The progeny or offspring of a mare.

Proportions:  The proportions of the horse's body: the relation between forequarters and hindquarters, the position and angle of the shoulder and pelvis to the forearm and gaskin, and the relationship between neck, back and length of croup.

Purebred:  A horse of a recognized breed whose male and female ancestors over many generations have all been registered animals.  (The term thoroughbred, not capitalized, which has often been used to designate this is inappropriate, since it may be with a Thoroughbred, which is only one example of a pure breed -- see T-Terms.)