BEECH MUSKETEER DEPARTED TXWY DURING TAXI OUT DUE TO LOSS OF DIRECTIONAL CTL BY STUDENT BEING GIVEN A FAMILIARIZATION FLT FROM A FLT INSTRUCTOR.

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INCIDENT OCCURRED DURING TAXI PHASE OF A FLT PRIOR TO DEP FOK. CONDITIONS WERE VFR SOME 10 HRS AFTER A SNOW STORM THAT DEPOSITED ABOUT 2-3 INCHES OF SNOW ON THE GND. WINDS WERE FROM 330 DEGS AT 11 KTS. TXWY WAS PLOWED AND IN GOOD CONDITION WITH ONLY VERY FEW SNOW/ICE PATCHES. PIC IS CFI IN A HIGH SCHOOL AVIATION PROGRAM TAKING 2 STUDENTS ON AN INTRODUCTION FLT FOR HAVING OBTAINED BEST SCORES IN THE CLASS FINAL EXAM. CFI WAS IN RIGHT SEAT. AS ACFT BEGAN TAXIING ALL WAS OKAY. BRAKES WERE CHKED AND FOUND OKAY. DURING TAXI; THERE WAS A SLIGHT TENDENCY FOR ACFT TO VEER TO THE RIGHT AND CFI ASKED STUDENT TO USE LEFT RUDDER AND LEFT BRAKE PEDAL AS NECESSARY TO KEEP ACFT ON TXWY CENTERLINE. THIS WAS ACCOMPLISHED SATISFACTORILY FOR ABOUT 1500 YARDS WITH STUDENT MANAGING FAIRLY WELL TO CTL ACFT WITHIN 3-4 FT OF THE TXWY CENTERLINE. CFI HELPED OUT WITH LEFT RUDDER ON (FIRST 90 DEGS) TURN TO THE LEFT AND STUDENT CONTINUED HOLDING WHAT I FELT TO BE LEFT RUDDER FOR CORRECTION. AT END OF FIRST TURN; ACFT WAS ON PROPER COURSE; VERY NEAR THE CENTERLINE AND THEN BEGAN TO VEER TO THE RIGHT AGAIN. CFI ATTEMPTED FULL LEFT RUDDER WHICH WAS ALREADY ON AND THEN LEFT BRAKE WHICH HAD LITTLE EFFECT. PWR WAS REDUCED TO 500-600 RPM AND ACFT CONTINUED TOWARD THE RIGHT SHOULDER OF TXWY. CFI'S APPLICATION OF BOTH BRAKES ONLY MADE MATTERS WORSE AS RIGHT BRAKE TURNED ACFT FURTHER TO THE RIGHT. CFI ASKED STUDENT TO GET OFF TH BRAKES AND RUDDER. CFI WAS ABLE TO MOVE ACFT BETWEEN TWO TXWY LIGHTS; AVOIDING ONE BY 2-3 FT. AFTER PUMPING THE BRAKES; LEFT BRAKE FUNCTION WAS ADEQUATE TO ALLOW NORMAL TAXI OPERATION AND TAXI RESUMED NORMALLY (WITHOUT THE STUDENT USING THE RUDDER PEDALS OR BRAKES) CFI DID REMAINING TAXI WITH RUDDER AND BRAKE USE. FLT WAS UNEVENTFUL; LNDG BY CFI AND TAXI BY CFI AT ARPT OF DEP WERE UNEVENTFUL AND 3 LEFT TURNS HAD T BE MADE FROM LNDG ROLL TO PARKING WITH NO PROB. (EXCEPT FOR A LOW LEFT BRAKE PEDAL). CONTRIBUTING FACTORS: FIRST FLT BY NEW STUDENT. CFI DID NOT REALIZE THAT STUDENT WAS USING 70-80 PERCENT LEFT RUDDER AND LEFT BRAKE DURING TAXI TO KEEP ACFT ON TXWY CENTERLINE. CONSTANT LEFT BRAKE PRESSURE BY STUDENT MAY HAVE RESULTED IN TEMPORARY RELEASE OF HYDRAULIC FLUID AD REDUCED LEFT BRAKE EFFECTIVENESS.