Here is some important horse vocabulary. Basic through hard words in no real order.
Bay: A light to dark brown horse with black lower legs, mane and tail

Buckskin: A horse with a coat of light flaxen, with a black mane and tail

Chestnut: Reddish-Brown

Dun: A pale beige horse, with black legs and a dark stripe along its back

Flaxen: Pale yellow

Roan: A bay, black or chestnut horse, with white hairs sprinkled on its coat

Piebald: A black horse with white patches

Skewbald: A horse of any shade, except black, with white patches

Blaze: A facial marking on a horse

Pack Pony: A pony used to carry loads

Driving Horse: A horse used to pull carts or carriages

Mare: A mature female horse

Stallion: A male horse used for breeding

Gelding: A male horse that has been gelded

Foal: A young horse that is still nursing

Colt: A young male horse no longer nursing but no more than four years old

Filly: A young female horse no longer nursing but no more than four years old

Mustang: A wild horse

Muzzle: The mouth, jaws, and nose of the horse

Barrel: The roundedsides of a horse, formed by the ribs

Dressage: A method of training horses often displayed at competitions

Hand: A unit of measuring a horses's height from hoof to withers, equal to 4 inches

Gaits: A horses different paces

Walk: A slow and steady gait about 3 to 4 miles per hour

Jog/Trot: A gait about 6 to 8 miles per hour where a rider might post if riding fast

Lope/Canter: A steady gait about 8 to 10 miles per hour

Gallop: Ths fastest gait about 25 to 30 mile per hour

Bridle: A harness for the horse's head, usually meaning the head stall, bit, and reins

Bit: The mouthpiece of a bridle

Reins: The leather strap attached toeach side of the bit , by which the rider controls the horse

Currycomb: A flat comb, usually round or oval shaped, for loosening dirt on a horse's coat

Dandy Brush: A brush used for making sweeping strokes across the horse's coat to remove dirt

Cinch: A starp that goes under the barrel of the horse  to secure the sattle

Hoof Pick: A curved pick used to remove debris impacted within the horseshoe of a shod horse

Neigh: Usually used by horses to let other know where they are, also called a whinny

Nicker: A gental call often used as a greeting to other horses and sometimes humans

Cavalry: A soldier on horseback

Polo: A game played on horseback

Rodeo: An American horse show at which cowboys display riding and herding skills