Complex sentence: Major mistakes, such as a rider going off-pattern, result in disqualification, sometimes called a "no score," which prevents the horse from earning any award, even if it is the only horse in the class.
Split into simpler sentences: Major mistakes, such as a rider going off-pattern, result in disqualification, (a score of zero). Both a zero score, and a no-score prevent the horse from earning any award, even if it is the only horse in the class.