Genetics 101, if I may!
Every living thing has genetic material in its cells. You string it all together and it's like one incredibly long sentence that reads basically: "This is how you make a _______ (example, horse.)
Every animal has two complete copies of that sentence, one that came from the mother, one from the father.
Genes are specific instructions in that sentence.
A trait (very simply) can be defined as something you can see about an animal (eye color, hair length, etc.)
Each trait has one gene that controls it.
Some genes come in more than one form. An animal that has only one form (both the one that came from the mother, and the one that came from the father, are the same) are said to be homozygous. Animals that have inherited two different forms of the same gene are said to be heterozygous.
A recessive gene is one that "takes a back seat" to the dominant form. The only way you see the results of a recessive, is if it is the only form present (homozygous for that gene).
A dominant gene is one that, if it is there, you will see the results. It only takes one copy of the dominant form, the other could be another dominant, or a recessive.
Dwarfism is thought to be the result of recessive genes. If that is the case, then the only way an animal can be a dwarf, is if it inherited a "dwarf gene" from both parents. If the parents are not dwarfs themselves, then they are heterozygous, having one dwarf gene and one normal gene. The normal gene is dominant, so the parents grew normally. Such animals are said to be carriers, having inherited the recessive, but not showing (expressing) it.
If a normal appearing animal has produced a dwarf, then you know it carries the recessive gene. It doesn't express it, because it also has the normal gene, which is dominant. Assuming this follows the normal pattern of inheritence, it makes no difference whether the animal is male or female, both parents must be carriers to produce the dwarf.
As I said, this assumes the normal pattern of inheritence. There are some weird ones! But if this understanding is correct, then any animal that produces a dwarf carries the dwarf gene. Every one of its offspring has a 50/50 chance of inheriting that gene.
If you breed two carriers together, your odds are 25% for a homozygous normal foal, 50% for a normal-appearing heterozygous foal, and 25% for a dwarf. That DOES NOT mean that you will get 3 normal foals for every dwarf this pair produces. It means that, if you could do this cross 100 times, about 25 of the foals would be dwarfs, and of the remaining 75, roughly two-thirds would be carriers. If you only did this cross say, 10 times, you could get 10 dwarfs, or no dwarfs, all homozygous, all heterozygous carriers, or any possible combination of the three.
Okay, retiring from the podium now. Did that make it any clearer? Or just more confusing?