PLT OBTAINED WX BRIEFING AND ADVISED OF KNOWN ICING CONDITIONS ALONG ROUTE. PLT FILED IFR FLT PLAN AND TOOK OFF AT 1733. AT 1744, PLT REPORTED PICKING UP RIME ICE AND REQUESTED LOWER ALT. ATC WAS UNABLE TO DESCEND PLT DUE TO MINIMUM VECTORING ALT AND TOLD PLT TO CLIMB TO 10,000 FT. AT 1745, PLT ADVISED HE HAD TOO MUCH ICE AND COULD NOT CLIMB. ATC CLEARED ACFT TO 9000 FT. AT 1748, PLT SAID HE WAS LOSING STATIC SYSTEM. ATC CLEARED ACFT DIRECT TO KIOWA VORTAC AND TOWARDS LOWER TERRAIN. AT 1752, PLT SAID HE COULD NOT MAINTAIN ALT AND WAS LOSING AIRSPEED. ATC CLEARED ACFT TO 8500 FT. AT 1753, RADAR CONTACT WAS LOST. AT 1756, ACFT CRASHED. TV VIDEOTAPES TAKEN 3 HRS AFTER CRASH SHOWED AT LEAST 1-IN RIME ICE ON LEADING EDGES OF WINGS, STABILIZERS, AND STRUTS. ACFT WAS NOT CERTIFIED FOR FLT INTO KNOWN ICING CONDITIONS. PLT WAS INSTRUMENT RATED, BUT HAD LOGGED ONLY 3.75 HRS IFR FLT, ALL ACTUAL, IN PREVIOUS 6 MOS.