Responsible breeders of miniature horses do not usually breed for "small." They breed for correct conformation, health, temperament, and soundness. Sometimes dwarf minis are born with horrible malformation, shortened legs, terrible mouths, crooked legs, large heads and roached backbones. Very often these do not live.
Others are born which are called "minimal dwarves." These have maybe one indicator of dwarfism, but do not have the entire malformations that others do. These can live with extra care.
Most breeders will not breed either the stallion or mare whose genetics produced the dwarf. They will have the stallion gelded and often give the mare to a pet home with the understanding she would never be bred.
Dwarves may NOT be registered.
Unfortunately, there are those who breed for small, small, small, and when a dwarf appears, they sell it as a curiosity, sometimes getting more money for it than a Mini foal with good conformation. Those people make me sick selling them as cute and strange little beings.
On the other hand, many responsible breeders, if and when they have a dwarf, they feel a responsibiltiy for its care and medical conditions for its lifetime. I know some very good farms have a dwarf which they care for with love and care because they produced it and care for the little animal. At times, a family might want a dwarf and do not mind the extra expense for medical care, but that is rare.
Dwarfism is unfortunate in minis, but it is a reality which breeders strive to keep from happening again. Studies and research are being done to isolate genes or gene markers for dwarfism. If that is done, genetic testing could be done to eliminate those with affected genes from the breeding herd.