I have a 12.2 shetland mare who can only carry up to 110 pounds. She is very very little, but she's great with children (on a lead line) I've been givig lessons to my lil cousin , and it work effectivly.
Im not saying all small horses/ponies are good for children, its just... well.... better.... closer to the ground lol. Im also not trying to say that all are easy to ride, it depends on the curcumstances.
So all in all, yes you can ride a mini, but putting a child on to ride I would not recomend.