Caravan C-FTZF was cleared for takeoff at Nakina (YQN) runway 09. Some 3/4 of the way through the takeoff run, a yaw to the right was experienced. This yaw was controlled and the aircraft lifted off the runway. The plane then began to yaw again and the pilot barely managed to control it. The Caravan descended, struck a frozen lake, flipped over and came to rest inverted approximately 1,000 feet past the end of the runway and 200 feet to the right of the extended right edge of the runway. CAUSES AND CONTRIBUTING FACTORS: “The pilot experienced directional control difficulties during the take-off run, probably because the rudder trim was set at the near full left position. Because the rudder trim indicator could be moved without affecting the actual rudder trim, it is probable that it did not reflect the actual position of the rudder trim.”