THE PILOT STATED THAT AT THE DEPARTURE AIRPORT, THE RUNWAY WAS SLIPPERY AND THE TURN ONTO THE RUNWAY WAS DIFFICULT. THE NOSEWHEEL STEERING WAS ACTIVATED MOMENTARILY TO STRAIGHTEN THE NOSE, BUT WAS TURNED OFF PRIOR TO THE TAKEOFF ROLL. AT THE DESTINED AIRPORT THE AIRCRAFT WAS LANDED AT APPROXIMATELY 115 KTS, AS SOON AS THE NOSEWHEEL TOUCHED, THE AIRCRAFT VEERED TO THE RIGHT. FULL LEFT BRAKE AND RUDDER DID NOT CORRECT THE SWERVE. THE NOSE GEAR STEERING ACTUATOR WAS EXAMINED AND NO EVIDENCE OF MALFUNCTION WAS REVEALED. ACCORDING TO THE COMPANY SAFETY BULLETIN AND AIRCRAFT MANUFACTURE BULLETIN, THE NOSE WHEEL STEERING SWITCH MUST BE OFF AND VERIFY THE NOSE WHEEL WILL CASTER (BY DISPLACING THE NOSE OF AIRCRAFT LEFT OR RIGHT USING BRAKES AND/OR ASYMETRIC ENGINE POWER) PRIOR TO TAKEOFF. THIS PROCEDURE IS TO BE PERFORMED BEFORE EVERY TAKEOFF WHILE TURNING ONTO THE RUNWAY. THE NOSE WHEEL STEERING MUST NOT BE ARMED UNTIL THE SUBSEQUENT LANDING IS COMPLETED AND AIRCRAFT SPEED IS REDUCED BELOW 10 KTS.