Ponyplay has inherent risks like many other practices in BDSM and life in general. However, ponyplay also has a subset of somewhat unique risks associated with it. I will assume that any ponyplay you are practicing is consensual since neither I nor this site condones any sort of non-consensual activity. If you know of any non-consensual activity, you should report it to the relevant authorities immediately.
There should be a safe signal during any ponyplay scene. Tapping with a hoof is a common safe signal. Three hoof taps might mean, "stop everything right now." Hand signals can also be used depending on the degree of restraint. Decide on a signal prior to a ponyplay scene that is easy to recognize. You should also make sure the pony can give this signal easily at all times during the scene. However, even with a safe signal in place, the trainer should be watching the pony for signs of over exertion, dehydration, etc. It is not unheard of for a pony to go past his limits without giving the safe signal, so the trainer should keep her eye out for any such signs.
It is important for the pony to be as comfortable as possible in his tack. Obviously bondage is going to carry a degree of discomfort no matter what, but don't overdo it. A good rule of thumb is the longer the scene, the less restrictive the bondage should be. I'm all for strict bondage, but I don't want to be tied with my elbows touching for several hours. Know your pony and his limits - find this out before you play!
Keep in mind that harnesses and collars can be restrictive to breathing. Combined with physical exertion, this can be quite dangerous. Tack that seems comfortable at first may become burdensome if worn for longer periods of time. Ponies that pull or carry loads should be especially careful with any tack that can restrict breathing. Moreover, even though bits leave the mouth open, they can press on the soft palate (if they sit far enough back in the mouth) and restrict the airway in that manner. It is very important to become acquainted with new tack slowly. Be especially careful with hoof boots, and any time a pony's arms are restrained.
Ponies being ridden should be sure that weight is distributed properly. Back and neck damage can occur.
Use common sense, know your limits, and don't be afraid to use the safe signal if you have reached your limits.
Above all, I would like to stress how important communication is between a pony and his trainer. Although she may be adept at reading your body language, it is critical that you discuss your hard and soft limits before a scene begins, and of course that a safety signal is established before you start a scene.