Size - sekelsta/horse-colors GitHub Wiki
Horses come in a wide variety of sizes, from tiny miniatures to giant drafts.
Effects of size
Smaller horse can fit in smaller spaces (sometimes even on boats!), while larger horses can carry more and have a higher base health.
Factors affecting size
Research into the genetic controls of size is still in the early stages. So far there are two tests available for genes affecting size:
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LCORL: normal or large. This is based on the Center for Animal Genetics' horse height test. The large variant is commonly found in draft breeds.
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HMGA2: normal or small. This is based on the Center for Animal Genetics' pony height test. The small variant is found in some Shetland ponies and related breeds, including miniature horses and the Welsh Mountain Pony.
Many other genes also affect size. It is believed that in horses, a small number of genes have a large effect (see here) and a large number of genes have a small effect (lay summary, another summary, study). That means there's a few genes that are very important to height, and lots that only barely matter.
Size is not entirely genetic. For instance, a horse with a small mother will not be able to grow as large before birth and will remain smaller its whole life. How much smaller is based on this study which crossed Shetland ponies with Shire horses. They found that the foal's birth weight depended mainly on the size of its dam. As it grew, its own size genes started to have more of an effect, but never enough to overcome the influence from its birth weight.
As of version 1.5.0, it should be pretty reasonable to breed down to 8.2 hands / 88 cm or up to 17.2 hands / 180 cm. It's trickier to breed down to 7.2 hands / 77 cm or up to 20.1 hands / 207 cm, and you can go a bit beyond that still but I really don't recommend it.
Donkeys
Donkeys are on average a bit smaller than the horses.