A stallion is a make adult horse over four years old. A gelding is a make horse that has been neutered. A colt is a young make horse. A sire is the word used for the father of a horse.
Females
A mare is a female horse over four years old. A filly is a young female horse. Dam is the word used for the mother of a horse.
General
A foal is a baby horse. A yearling is a horse between one and two years of age. A pony is not a baby horse, it is a fully grown small horse!!!