DURING THE PREVIOUS FLT, THE ACFT ENCOUNTERED LIGHT ICING CONDITIONS WHILE CRUSING AT 4000 FT. THE CAPT STATED THAT THE ICE DISAPPEARED FROM THE ACFT'S STRUCTURE IN THE COURSE OF ITS DESCENT AT 3000 FT & HE DID NOT USE WING DE-ICING OR THE ENG COWLING DE-ICE/ANTI-ICE SYS. THE ACFT ARRIVED AT JFK INTL ARPT AT 1346 EST. DURING A PREFLT FOR THE NEXT FLT, THE CAPT NOTED WHAT HE DESCRIBED AS A WHITE LINE OF ICE ON THE LEADING EDGES OF BOTH WINGS, APRX 1-1/2' WIDE & LESS THAN 1/16' THICK. HE DID NOT GET A LADDER TO CHECK THE ENG INLETS. FOR TAKEOFF AT 1442, THE ENG DE-ICE/ANTI-ICE SYS WAS TURNED ON; HOWEVER,IT WOULD NOT HAVE ACTIVATED UNTIL THE WT WAS OFF THE GEAR. DURING GEAR RETRACTION, THE L ENG LOST PWRWHICH WAS FOLLOWED BY A R ENG PWR LOSS. SUBSEQUENTLY, THE ACFT WAS LANDED ON THE RWY WITH THE GEAR IN TRANSIT TO THE DOWN POSITION. THE ACFT THEN SLID OFF THE RWY & INTO SNOW. THERE WAS EVIDENCE THAT BOTH ENGS HAD LOST PWR DUE TO INJESTION OF ICE THAT HAD ACCUMULATED DURING THE PREVIOUS FLT.