An intact horse is one that retains its reproductive organs and full capacity to breed. The term is most frequently applied to male horses: a intact stallion management is an intact male, whereas a gelding as the alternative has been castrated and is no longer intact. An intact female — a mare — is not typically described by this term, though the word is sometimes used to confirm that a mare has not been surgically sterilised.
Intact males exhibit hormonal behaviours — heightened aggression, vocalisation, and interest in mares — that make management more demanding than with geldings. Most performance and pleasure horses are gelded to reduce these behaviours and simplify herd integration. Breeders keep stallions intact to pass on desirable traits; the decision requires facilities that prevent unplanned contact with mares and fillies. The word intact is also used in a wound-assessment context to confirm that a skin surface or anatomical structure (tendon sheath, joint capsule) is unbroken, which carries direct prognostic significance.
Further Reading
The contrast between intact and castrated males is addressed in the castration article on Wikipedia, which covers the procedure and its physiological effects in horses. Reproductive management of intact horses is covered in the Merck Veterinary Manual section on Reproductive Disorders of Horses.