Minis can be great I don't think that you can say any type of horse is good or bad it just depends on the horse. We have had horses for over 30 yrs. and I have had good, bad and rotten of all kinds. I think that you need to find the right horse for your child. An older mini that is trained would be best for a young child. My kids are 5 & 9 we have small horses 14 hands and 13.3 hands and those are my kids horse but we also have a 16 hand horse that I trust with any child. My daughter was in a dressage show a few wks back and she rode and 8 hand pony, and she is not for begginers or little kids because she is a stinker when being ridden. We also use her for vaulting and she is great and is best for the little kids. So I think it just depends on the mini/horse that you are looking at and what you will use it for. Here is a pic of my daughter at the horse show.
