I have ridden a standard shetland, but hasten to add I am very small and lightweight, and backed small ponies for people who are to big to do it themselves. But, to be honest, mini shetlands are really pets.companions.....but yes, they can be ridden, and even driven.
You do need to get the pony used to a saddle, but no point in a bridle if you are just lead reining. Once you are sure the saddle is no problem, then you can pop a child on, just standing still, and gradually walking a little. I am sure your pony will be fine, as it sounds well handled.
Its just before putting a child on, I would like to make sure myself it was safe, but obviously being that small, its impossible for an adult to do this.