You can drive an ATV on private land at any age (with the owner's permission). If a child is age 10 through 15, they must have adult supervision or ride on land owned or rented by their parent or guardian without adult supervision. Additionally, children between 10 and 15 can operate an ATV on land where ATV use is permitted without adult supervision if they have completed an ATV safety training course. Children under the age of 10 can operate an ATV if they are under adult supervision.
Check out these Troy, NY ATV/OHV resources: