"The Pretty Pony Steeplechase, featured in Barnum & Bailey's 1906 lineup, depicted diminutive Shetland ponies with chattering monkey jockeys racing around the hippodrome track at top speed over pint-sized obstacles. This was a great favourite of the children in the audience."
we have three minis... we have found they best used for introducing the kids to the horses. We do drive them (the minis, not the kids), training was just hooking to the cart ...they are a natural at driving
A 36" mini is 9 hands, right? So little, but not ridiculously tiny. I used a Shetland pony that small for pony club games when I was 8 or 9-- she went to PC Nationals and everything So it can be done. That pony was EVIL, too. I can't imagine she was just broke by leading a kid around. There was definitely a small adult or teenager involved. If there is a pony breeder in your area maybe call them for ideas?
It really depends upon your mini's build and your son's weight. At 36 inches, if your mini is sturdily built and your son is small, it shouldn't be a problem for light riding for short lengths of time. For a 36 inch mini, I wouldn't let a child over 70 lbs or so ride. I would never let an adult of any size ride a 36 inch mini of any build.
We've put a toddler on my very refined 38" gelding with a parent right there to grab them, and Mingus, who had never before been ridden, took to it as if he had done it forever. He was so careful, using his back muscles to keep his rider in place.
I would train your horse to ground-drive and respond well to both rein and verbal cues first, using a saddle and running the lines through the stirrups. Once he is used to the saddle, a small child won't be that much more weight. Get another adult to set your son in the saddle (or let them hold he horse while you lift your son), being prepared to lift him off if there are any problems. I would do leadline at first while your son learns to balance and your mini gets used to his rider, then depending upon your horse's behavior, slowly let him use the reins.
Most minis are used for leadline rather than for actual riding, but that can be a good way to get a child comfortable on horseback, even if it is for a very short tine.
I second the idea of training your mini to drive -- he's big enough to take you and your son for a drive, and you can all enjoy this for a long time to come!