While most human ponies are cart ponies, riding ponies, show ponies, rubber ponies, or any combination thereof, there are still many other types of ponies and even more subtypes. So while I cannot cover all of them here, I will try and discuss a few more types that are seen enough in ponyplay to not be uncommon.
Working ponies/horses are also referred to as draft ponies/horses, pack ponies/horses. While all ponies need to have some athletic ability to carry a rider, pull a cart or show off their gaits, working ponies are trained specifically for athletic ability. Working ponygirls or ponyboys are trained to pull heavy loads over longer distances and over rough and terrain and obstacle courses. The working pony is trained just like a real work horse, and can pull loads of rock, wood, etc. Working ponies can also be used to move heavy objects blocking paths and trails, such as branches or small trees. These ponies typically have utilitarian tack and are very much about function instead of appearance. Working ponies are also trained to work blindfolded, and there are working pony shows where the ponies will pull a heavy load through an obstacle course while blindfolded. In addition to testing athletic ability, this type of show also tests how well a pony can interpret non-visual cues, and how sensitive a pony is to the aids (such as the reins).
Breeding ponies are ponies that are, well, meant to be bread. Breeding ponies breed with other ponies; this can involve actual sex, or it can simulate breeding. Breeding scenes, especially those involving actual sex are agreed upon by the ponies involved prior to entering pony role.