There are three kinds of dwarfism in horses:
1. Skeletal atavism. This is seen in Shetland ponies - it results in short legs, a stocky body and a pot belly. Shetland ponies are the only dwarf breed of equine.
This Shetland pony looks even fatter due to being out in the middle of winter (source: Miles Wolstenholme via Wikimedia Commons). The pic clearly shows the short legs and pot belly (it's possible this is also a pregnant mare, so it's a wee bit exaggerated).
These horses are perfectly healthy - they're simply a dwarf breed. In fact, there may be a connection between skeletal atavism in equines and longevity - Shetland ponies are well known for being long lived. (Not to mention being strong enough to pull twice their own weight).
2. Achondroplastic dwarfism. This is a completely different thing and the bane of breeders of miniature horses. It's caused by one of four different genetic complexes, all of which are recessive. (They can now be tested for).
This is an achrondoplastic dwarf (image source Phil Konstantin via Wikimedia commons). As you can see, she also has the pot belly and short legs. However, she has a bulging forehead and weak hind legs.
Achrondoplastic dwarfism is associated with early pregnancy loss. Surviving foals may have breathing problems, malformed mouths and abnormal bone growth. Responsible breeders often euthanize dwarf foals.
3. Osteochondrodysplasia. This form of dwarfism is found in Friesian horses and is also associated with health problems, specifically weakness in the tendons in the legs.
(Sadly I was not able to find a good picture).
I will be at RavenCon in Richmond this weekend and will be doing a short presentation related to this blog (thank you convention admin). It will be in the boardroom at noon on Sunday.