Guess it depends on the size of the pony (all horses under 14.2 hh are considered poines), the weight and athletic prowess of the child, the speed of the ride, and exactly what you mean by “ride” (led around by an adult, for example, or something else).

@Pachyderm_In_The_Room
Perfect

With any riding activity, make sure it is done someplace reputable – make sure the rider wears a helmet and is properly supervised. A small child can be lead around on a horse or pony but some horses or ponies have a temperament more suitable for this than others. Explain to the child that it is important to follow the instructions that the person leading them gives (while on and off the horse—such as no running or shouting when dismounted…).