THE AIRCREW TOOK OFF ON AN IFR FLT FROM DAYTON TO PIQUA & SIDNEY, OH TO PRACTICE APCH'S, THEN THEY INTENDED TO RETURN TO DAYTON. THE COPILOT STATED THAT THEY ENTERED THE CLOUDS AT 700 TO 800 FT AGL & HE DID NOT SEE THE GROUND AGAIN ON THIS FLT. HE REPORTED THAT ICE BEGAN BUILDING ON THE ACFT UNTIL ON A DESCENT TOWARD PIQUA, WHEN REPORTEDLY, IT BEGAN DISSIPATING. A MISSED APCH WAS MADE AT PIQUA WITHOUT SEEING THE ARPT. THE COPILOT STATED THAT THEY WERE UNABLE TO GET A GOOD RATE OF CLIMB. AT 1258 EST, THE AIRCREW REQUESTED VECTORS BACK TO DAYTON (RATHER THAN TO CONTINUE TO SIDNEY) & ADVISED THAT THEY WERE ENCOUNTERING ICE & TURBULENCE. THEY WERE ISSUED A VECTOR, BUT APRX 30 SEC LATER, THEY ADVISED THAT THEY COULD NOT MAINTAIN THEIR ASSIGNED ALT OF 3000 FT. THEY WERE ADVISED THAT VECTORS COULD NOT BE PROVIDEDBELOW 3000 FT, BUT THE SIDNEY ARPT WAS AT THEIR 2 O'CLOCK POSITION AT LESS THAN A MILE. SHORTLY AFTER THAT, THE ACFT CRASHED IN A WOODED AREA APRX 1 1/2 MI WEST OF THE ARPT. REPORTEDLY, RAIN WAS ENCOUNTERED BETWEEN PIQUA & SIDNEY.