While in cruise flight, the 19,620-hour commercial pilot lost control of the rudder pedals and experienced trouble maintaining directional control of the single-engine, turbine powered agricultural airplane. The pilot reported that "he dumped his chemical load at a safe location" and elected to discontinue the aerial application flight. The pilot proceeded to a larger airport for a landing. The pilot added that he made several attempts to land as he was having trouble keeping the airplane aligned with runway 35 unless he maintained a much higher than normal airspeed on final approach. On his final attempt, the pilot was able to land, but as the airplane slowed down, it veered off the right side of the 5,949-foot long, by 75-foot wide asphalt runway. Following the loss of control, the left wing of the airplane collided with a tractor. A Federal Aviation Administration (FAA) safety inspector performed an on-scene examination of the airplane and found that the rudder horn was corroded and had completely separated. According to the pilot, the rudder horn is covered by fabric and it was difficult to inspect during a preflight inspection. The pilot added that even though the operator has a procedure in place to wash the airplane after spraying corrosive chemicals, he suggested that somehow chemicals had made contact with the rudder horn which caused the corrosion. At the time of the last 100 hour inspection, which was completed less than 11 days prior to the mishap, the tailwheel-equipped airplane had accumulated a total of 11,107.8 hours since new. The wind at the time of the accident was reported from 030 degrees at 8 knots.