The idea that the large heart is passed through the X chromosome leads one to several interesting conclusions. First of all, a brief discussion of genetics is in order to help explain the theory. Females have 2 X chromosomes, and males have one Y and one X chromosome. The chromosomes are a genetic road map that exactly describes every attribute. The X chromosome is larger and therefore has more space for the genetic markers that describe traits.
Many traits are a function of markers from both chromosomes.
Heart size, however, based on research carried out by Marianna, and others, seems to be carried on the X chromosome alone. Thus a male horse has a single marker for heart size, while a female has two. A female offspring inherits the X chromosome from both parents. So a male horse has one chance of a large heart. He inherits one of two chromosomes from his dam, and that determines his heart size.