WHILE IN CRUISE FLIGHT AT 3,000 FT THE PILOT REPORTED TO ATC THAT THE ENGINE WAS LOSING OIL PRESSURE. WHILE BEING VECTORED TO AN AIRPORT, THE PILOT REPORTED 'ENGINE'S GOING'. WITNESSES OBSERVED SMOKE COMING FROM THE AIRPLANE, AND A SPUTTERING ENGINE NOISE. THE ENGINE NOISE CEASED AND THE AIRPLANE WAS OBSERVED TO PITCH UP, BANK LEFT, AND IMPACT A TREE. EXAMINATION OF THE ENGINE REVEALED OIL STARVATION DUE TO A RUPTURED OIL COOLER LINE. THE LINE WAS DETERIORATED NEAR THE AREA CLOSEST TO THE EXHAUST STACK. MAINTENANCE LOGS WERE NOT RECOVERED.