IMO size of the operator is almost as important as age. You can be 20 and if you don't fit the equipment properly i.e. too short to fully depress pedals, too weak to turn steering etc. you increase the risk for 'opportunities' to occur. Age is really a matter of maturity. Operation of a mower can be fun but with the blade spinning, it is dangerous if the operator is inattentive or playing or even hurrying to get the job done.
Having said that, it is also a great way to teach responsibility, safety and vehicle maintenance. There are many pre teens helping on the family farm using equipment much larger then a riding mower.
Again, this is just my opinion.