In pony play the slave is typically either dressed in bit and bridle like a horse, or she moves on hands and knees and is ridden like a pony by her Master or Mistress. Hence, the slave being treated like a horse is called the pony slave.
In some types of pony play the slave is made to wear an elaborate harness and bridle. With the bit in her mouth she is unable to speak, and must respond to the reigns that her Master or Mistress holds. In outdoor pony play, slaves may also be attached to a light carriage and be forced to pull their owner.
The other style of pony play is where the slave (again, usually wearing the pony's harness) is kneeling on her hands and knees. In this position, the Master or Mistress will sit on the slave's rump and ride her around the room. Saddles and other horse paraphernalia are common equipment.
Naturally, pony slaves are often slow or misbehave, so Masters and Mistresses usually bring along a riding crop. Just in case.