DURING A MULTI-ENGINE TRAINING FLIGHT, THE INSTRUCTOR PILOT SAID HE SHUTDOWN THE LEFT ENGINE. AN ENGINE RESTART WAS UNSUCCESSFUL AND AN EMERGENCY LDG WAS INITIATED. EMERGENCY GEAR EXTENSION PROCEDURES WERE ATTEMPTED; HOWEVER, GEAR DOWN AND LOCKED INDICATIONS WERE NOT SEEN BY THE PILOT AND HE DECIDED TO LAND IN A PLOWED FIELD. ON THIS MODEL OF ACFT, THERE IS ONLY ONE HYDRAULIC PUMP WHICH IS ON THE LEFT ENGINE. THE NORMAL GEAR RETRACTION/EXTENSION IS HYDRAULICALLY OPERATED.