C172 STUDENT PLT WAS SOLOING FOR THE FIRST TIME ON A 40 FT WIDE RWY. SNOW AND ICE WAS BLOCKING SOME OF THE RWY WIDTH. THE STUDENT PLT HIT THE SNOW AND LOST ACFT CTL.

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I AM A FLT INSTRUCTOR THAT SENT A STUDENT ON HIS FIRST SOLO FLT. PRIOR TO THE EVENT; WE HAD COMPLETED 5 TRIPS IN THE PATTERN. THE AREAS THAT WERE REVIEWED INCLUDED: 1 GAR PRACTICE PROC FOLLOWED BY 4 NORMAL TKOFS/LNDGS; TAXI PROCS; BRAKING CONDITIONS; ACFT PERFORMANCE/SPDS; WIND CORRECTION; CHKLIST PROCS AS WELL AS MAINTAINING THE RWY CTRLINE. THE STUDENT IS CURRENT AS FAR AS FAR 91/61 DOCUMENTS AND PROCS ARE CONCERNED. I FELT THE STUDENT PLT (17 HRS) WOULD BE ABLE TO CONDUCT THE FLT IN A SAFE MANNER AND ASKED HIM IF HE FELT COMFORTABLE IN COMPLETING 2 TRIPS AROUND THE PATTERN BY HIMSELF. HE INFORMED ME OF HIS CONFIDENCE AND TOLD ME HE WOULD BE COMFORTABLE. I EXITED THE ACFT AND SENT HIM ON HIS INITIAL SUPERVISED SOLO. UPON THE LNDG ROLL (XA15 LCL); I WITNESSED THE ACFT VEER L APPROX 500 FT AFTER TOUCHDOWN AND PIVOT ON THE L WHEEL INTO THE 'KNEE-DEEP' SNOW EDGING THE RWY. THE ACFT WAS IMMEDIATELY SHUT DOWN AND THE STUDENT PLT EXITED SAFELY. ONCE ARRIVING TO THE ACFT/STUDENT; I FOUND HE HAD NO INJURIES AND WAS GOING TO NEED ASSISTANCE PULLING THE ACFT OUT OF THE SNOW. THE L WHEEL RUBBED A RWY LIGHT WHICH WAS INSPECTED SHORTLY AFTER BY THE COUNTY AND WAS EASILY FIXED AT NO COST (NO DAMAGE). WE NOTIFIED FSS AND HAD THE ARPT TEMPORARILY CLOSED UNTIL THE ACFT WAS REMOVED FROM THE SNOW AT APPROX XA34 WHEN WE RE-OPENED THE ARPT WITH FSS. I SAT DOWN WITH THE STUDENT AND DISCUSSED WHAT HAD HAPPENED. HE TOLD ME THAT HE HAD A GREAT FLT AND WAS VERY COMFORTABLE UNTIL THE LNDG ROLL. 'THE ACFT WAS DRIFTING TO THE L AND I APPLIED R RUDDER AND R AILERON TO CORRECT. THE RUDDER WAS UNRESPONSIVE AND THE L MAIN WHEEL OF THE ACFT CAUGHT THE SNOW AND PULLED ME OFF THE RWY.' I BELIEVE THE STUDENT LANDED L OF THE CTRLINE AND FOUND THE ACFT DRIFTING L. HE APPLIED UNEQUAL BRAKING BY FAVORING THE L SIDE WHICH HELPED THE ACFT DRIFT FURTHER FROM THE CTR. THE RWY HAD A 6 FT TREAD MARK LEADING INTO THE SNOW. ONCE THE L MAIN WHEEL CAUGHT THE EDGE OF SNOW; IT WAS EASILY PIVOTED APPROX 30 DEGS L AND STRUCK THE SIDE OF A RWY LIGHT. AS A PRECAUTION; I HAVE DECIDED TO GND THE ACFT UNTIL A CERTIFIED MECH CAN MAKE THE APPROPRIATE CHKS NEEDED FOR SAFE FLT. THE STUDENT HAS DECIDED TO CONTINUE FLYING AND THE APPROPRIATE GND SESSIONS WERE CONDUCTED. I INFORMED HIM THAT EVENTS WILL HAPPEN AND WE HAVE LEARNED FROM TODAY'S EXPERIENCE. I HAVE NO DOUBT HE WILL CONTINUE FLYING AND EARN HIS PVT PLT CERTIFICATE AND BE A SAFE PLT. SUPPLEMENTAL INFO FROM ACN 605969: SHORTLY AFTER THE TOUCHDOWN; THE C172 STARTED TO DRIFT TO THE L. THE ATTEMPT TO CORRECT THE PLANE ONTO A STRAIGHT COURSE WITH THE R RUDDER/BRAKE FAILED; DUE TO ICY CONDITIONS ON THE RWY. THE MORE THE PLANE CAME UP FROM THE CTRLINE; THE WORSE BECAME THE CONDITIONS (SNOW/ICE) ON THE RWY. I ATTEMPTED TO PREVENT THE CESSNA FROM LEAVING THE RWY BY APPLYING FULL BRAKES (L AND R). THE L TIRE THEN CAUGHT IN DEEPER SNOW; WHICH DIRECTED THE CESSNA FURTHER L. I WAS NOT ABLE TO KEEP IT ON THE RWY. I AM CONCLUDING THAT THE AMOUNT OF BRAKE FORCE APPLIED WAS NOT APPROPRIATE FOR THE CONDITIONS ON THE RWY. THE INCIDENT COULD HAVE BEEN POSSIBLY PREVENTED BY APPLYING R RUDDER ONLY; AND NO BRAKE FORCE TO STEER PLANE BACK ON CTRLINE OF THE RWY. THE ICY PAVEMENT OF THE RWY; ESPECIALLY OFF THE CTR; MADE IT IMPOSSIBLE TO CTL THE AIRPLANE; ONCE IT GOT TOO FAR TO THE L.