You get an X from mom and an X or Y from dad. So maybe dad is more influential since he determines gender? I don’t know about the mitochondria, it’s been 30+ years since I’ve had any bio or chem. Genetics is so complex; you have dominant and recessive genes and many other factors. Plus, each foal is independent of all previous and any subsequent foals. It’s like a coin flip - just because you had heads 7 times in a row doesn’t mean you’ll have tails the next flip. It’s always a 50/50 chance.
As I understand it, each gene has a 50/50 chance of transmitting from either the mother or the father. That doesn’t mean that 50 % of the genes are always from the mother and 50 % from the father. That’s why in a family of 5 human children, they can all look different: hair color, height, eye color, aptitudes, especially if the parents don’t look a lot alike.
5 foals from the same stallion and mare combo could also turn out quite different. If you are keeping it within one breed the whole family will be more similar than any human family, all second and third cousins. They will look similar but they won’t all necessarily perform as well.
But if you were mixing say Clydes and TBs, which is more the human situation (genetically unrelated marriage) you could get a wide variety of foals. One could be a smaller draft horse, one could be a nice hunter with good bone. Depends on the genetic lottery.
I don’t remember much about the mitochondria either and besides genetic science has grown exponentially since I was in school. I realize the more they discover, the more complex the questions become about expression, epigenetics (when the environment causes a gene to switch on), how genes interact, etc.
But to say that there is a 50/50 chance of a baby or a foal being male or female, for Instance, doesn’t mean that in any given family or breeding program you will get half and half. Back when people had bigger families I recall a few with 4 or 5 daughters and then the youngest, a son, at which point they stopped “trying.”
I went to research what I thought I knew, and it’s a lot more complicated 
https://www.eupedia.com/forum/threads/25375-Genetic-inheritance-why-people-can-be-closer-to-one-parent-than-the-oher-genetically
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Yeah, my head is swimming. It takes more than a quick read to digest that information.
Edit to add: The thing that I keep reflecting on from your article is this comment:
Sisters are even closer to each others because they have one full identical X chromosome (inherited from their father), which is bigger than a Y chromosome. Their second X chromosome is also an random admixture.
It does reinforce the practice in horse breeding of looking at full sisters for good nicks.
