When a horse has small nostrils, the opening of the nostrils (the nares) is narrow and somewhat restricted, limiting ability to expand the nostrils for breathing while working hard.
This may occur in any breed. It especially affects horses in high-speed activities (polo, racing, eventing, steeplechase) or those that need to sustain effort over long duration (endurance, competitive trial, combined driving). These horses are therefore best for pleasure-riding or non-speed sports.
Small nostrils are often seen in horses that also have narrow jaws and a narrow muzzle.