INSTRUCTOR PLT; WITH STUDENT FLYING; FAILED TO HOLD SHORT OF RWY INTXN AFTER LNDG DUE TO LONG LNDG BY STUDENT AND THE INSTRUCTOR NOT HEARING THE LAHSO IN THE LNDG CLRNC.

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ACFT WITH CFI AND STUDENT PLT ON BOARD WAS RETURNING TO GSO FROM LCL AREA FLT. ACFT ACCEPTED CLRNC TO LAND ON RWY 14 AND HOLD SHORT OF RWY 23. STUDENT PLT ACKNOWLEDGED CLRNC. HOWEVER; CFI MISSED INSTRUCTIONS TO 'LAND AND HOLD SHORT' DUE TO UNKNOWN REASONS/DISTRS NORMALLY ASSOCIATED WITH TRAINING ENVIRONMENT (USE OF INTERCOM; OTHER XMISSIONS). STUDENT FLEW ACFT TO SHORT FINAL APCH; MISJUDGED ALT AND ACFT WAS SLIGHTLY ABOVE NORMAL GS AND AT HIGHER THAN NORMAL APCH SPD. AT ABOUT 100 FT AGL NEAR APCH END OF RWY 14; THE CFI ADVISED THE TWR THAT THEY WOULD BE 'LNDG LONG' OR SOMETHING TO THAT EFFECT. NO ACKNOWLEDGEMENT WAS RECEIVED FROM THE TWR. THE CFI WAS STILL UNAWARE OF THE 'LAND AND HOLD SHORT' RESTR AND THE STUDENT PLT MADE NO COMMENT REGARDING CLRNC. TURB; XWINDS; AND VERT UP-/DOWNDRAFTS ADDED TO THE WORKLOAD. THE ACFT WAS LANDED AND ROLLED THROUGH THE INTXN OF RWYS 14 AND 23 THEN TURNED TO CLR THE RWY AT THE FIRST TURNOFF TO THE R PAST RWY 23. THE CFI NOTIFIED THE TWR THAT THE ACFT WAS CLR THE RWYS AND REQUESTED TO TAXI TO THE FBO. THE TWR THEN ADVISED THE CFI/STUDENT OF THE SIT; IE; EXCEEDING THE CLRNC RESTR. NO TFC CONFLICTS WERE EXPERIENCED (FORTUNATELY). CONTRIBUTING FACTORS: CFI MISSED LAHSO CLRNC/ADVISORY DUE TO POSSIBLE DISTRS RELATED TO INSTRUCTION. STUDENT DID NOT MENTION RESTR TO CFI. ALTHOUGH CFI ADVISED TWR OF INTENT TO 'LAND LONG;' NO RESPONSE/ADVISORY; ETC WAS RECEIVED FROM THE TWR UNTIL AFTER LNDG ROLLOUT WITH ACFT ON TXWY. STRONG/GUSTY WINDS (AND XWIND) ADDED TO WORKLOAD. XMISSIONS OVERHEARD DURING LNDG ROLLOUT WERE BROKEN UP AND MAY HAVE INDICATED RECEPTION PROBS. HOWEVER; STUDENT PLT HAD KNOWLEDGE OF RESTR -- CFI DID NOT. CORRECTIVE ACTIONS: CFI AND STUDENT PLT HAD IN-DEPTH DISCUSSION OF EVENT CONTRIBUTING FACTORS; AND POSSIBLE PREVENTIVE MEASURES TO PRECLUDE SIMILAR RECURRENCES. CFI REQUESTED DISCUSSION WITH ATC CTLR; VISITED FACILITY; AND SUBSEQUENTLY DISCUSSED THE SIT/CONTRIBUTING FACTORS AND CORRECTIVE MEASURE IN DEPTH.