THE PLT REPORTED THAT WHILE HE WAS MAKING AN INSTRUMENT APCH IN HEAVY RAIN, THERE WAS A PARIAL LOSS OF ENG POWER. HE APPLIED CARBURETOR HEAT, BUT REPORTED THAT THE ENG STILL DID NOT PROVIDE FULL POWER. HE CONTINUED THE VOR/DME APCH. WHEN HE SAW THE RWY, HE DECIDED THAT HE WAS TOO HIGH TO LAND. REPORTEDLY, HE ENTERED A DOWNWIND & LANDED WITH FULL FLAPS ON RWY 32. THE PLT STATED THAT HE WAS TOO FAST, AND THAT AFTER TOUCHDOWN, THE ACFT BEGAN HYDROPLANING. SUBSEQUENTLY, THE PLANE CONTINUED OFF THE END OF THE RWY, HIT A DITCH & NOSED OVER. THE PLT REPORTED THAT HE DECIDED NOT TO GO AROUND SINCE HE CONSIDERED THE ENG WAS UNRELIABLE & THERE WERE HIGH OBSTRUCTIONS OFF THE END OF THE RWY. HE REPORTED THE WIND WAS FROM 070 DEG AT 6 KTS. APRX 55 MI EAST AT ROLLA, MO, THE 1148 CDT WX WAS, IN PART: 600 SCT, 6000 OVC, VSBY 5 MI WITH FOG, WIND 160 DEG AT 10 KTS, TEMP 64, DEN POINT 62. ACCORDING TO ICING PROBABILITY CHARTS, SERIOUS CARBURETOR ICING COULD BE ENCOUNTERED AT CRUISE POWER WITH FLOAT TYPE CARBURETORS.