New York State Route 10 is is a north-south highway in Hamilton County. It runs from the Hamilton/Fulton County Line, near Caroga, to New York State Route 8, at Arietta. NY St Rt 10 passes through the following town in Hamilton Coumty. Arietta NY St Rt 10 is not multi-plexed in Hamilton County. NY St Rt 10 intersects the following highway in Hamilton County. New York State Route 8, at Arietta.