WITNESSES REPORTED THE AIRPLANE WAS IN A WIDE SPIRAL, THEN IT SUDDENLY ENTERED A DIVE & CRASHED. ONE WITNESS, WHO WAS OUTSIDE & AWAY FROM STRUCTURES, REPORTED THE ENGINE WAS SPUTTERING, JUST BEFORE IMPACT. THE DUAL STUDENT RETAINED ONLY A FRAGMENTED MEMORY OF THE DAY OF THE ACDNT. HOWEVER, HE REMEMBERED THAT THE INSTRUCTOR TOOK CONTROL OF THE AIRPLANE, WHEN THE ENGINE BEGAN TO SPUTTER DURING A POWER APPLICATION. ALSO, HE REPORTED THAT CARBURETOR HEAT HAD BEEN USED PRIOR TO APPLICATION OF POWER. A REVIEW OF THE INSTRUCTOR & STUDENT LOGBOOKS SHOWED THAT THERE HAD BEEN INSTRUCTION IN EMERGENCY PROCEDURES DURING THE PREVIOUS PERIOD OF INSTRUCTION. NO PREIMPACT PART FAILURE WAS FOUND DURING THE INVESTIGATION. THE ENGINE WAS MOUNTED ON A TEST STAND & OPERATED TO 1000 RPM. THE TEMPERATURE & DEW POINT WERE REPORTED TO BE 54 & 47 DEG, RESPECTIVELY. ACCORDING TO ICING PROBABILITY CHARTS, CONDITIONS WERE CONDUCIVE TO SERIOUS ICING AT CRUISE POWER.