STUDENT PLT RUNS OFF SIDE OF RWY DURING A FINAL PHASE CHK. RWY EXCURSION.

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THIS OCCURRENCE TOOK PLACE WHILE I WAS ACTING AS AN INSTRUCTOR FOR A STUDENT PLT ON HIS FINAL PHASE CHK PRIOR TO HIS PRIVATE ORAL/FLT TEST. THE STUDENT HAD APPROX 30 HRS OF DUAL INSTRUCTION (WITH ANOTHER CFI) AND 20 HRS OF SOLO FLT PRACTICE PRIOR TO THIS FLT; THAT THE STUDENT CONSISTENTLY FELT THAT ANY SUBSTANDARD PERFORMANCE WAS ACCEPTABLE AS LONG AS IT WAS WITHIN HIS LIMITS (I.E. HOLDING A CONSTANT ALT IS NOT IMPORTANT; LNDG OFF THE RWY CTRLINE IS OK; ETC. AFTER SOME AIR WORK WE FLEW TO THE RICHMOND; RI; ARPT (RI04) FOR SOME SHORT FIELD TKOFS AND LNDGS. AN INCH OR SO OF FRESH; SOFT SNOW WAS PRESENT ON THE SIDES OF THE RWY. THE PLOWED; ASPHALT RWY WAS CLR AND DRY. A NORMAL TFC PATTERN AND APCH WAS MADE. A SLIGHTLY HIGHER THAN NORMAL FLARE WAS INITIATED BY THE STUDENT AND THEN HE BEGAN TO ALLOW THE PLANE TO DRIFT TO THE L OF CTRLINE. THE ACFT CONTINUED TO DRIFT TO THE L AND THE STUDENT DID NOT MAKE ANY CORRECTIONS -- LIGHT WINDS. THE STUDENT WAS NOT CONCERNED AS THE L MAIN WHEEL WENT OFF THE RWY AND INTO THE SNOW. THE ACFT CONTINUED TO MOVE OFF THE RWY INTO THE SNOW AND SLOWLY CAME TO A STOP. THE ENG WAS SHUT DOWN AND THE ACFT PUSHED BACK ONTO THE RWY BY HAND. AN INSPECTION OF THE ACFT AND ARPT WAS MADE. HAVING OPERATED AT RI04 FOR SEVERAL YRS; I KNEW THAT THE RWY LIGHTS WERE DISPLACED FROM THE RWY EDGES AND THAT THE ADJACENT GND WAS LEVEL AND IS USED FOR ULTRALIGHT OPS. INJURIES -- NONE. DAMAGE TO ACFT -- NONE. DAMAGE TO ARPT -- NONE.