THE ACRT CRASHED IN A PASTURE AFTER FUEL EXHAUSTION DURING AN APPROACH TO JOHNSON COUNTY INDUSTRIAL ARPT. THE ACFT HAD MADE A MISSED APPROACH AT HIS DESTINATION OF NEVADA MO. ENROUTE TO A SUGGESTED ALTERATE OF BUTLER ARPT. THE WEATHER BECAME WORSE AND JOHNSON COUNTY BECAME THE VIABLE ALTERNATE. DURING THE APPROACH THE ACRT RAN OUT OF FUEL. AFTERTHE ACRT DESCENDED OUT OF THE CLOUDS IT IMPACTED RIGHT WING AND NOSE LOW IN A PASTURE. IT THEN SPUN AROUND AND SLID BACKWARDS INTO A FENCE. THE PILOT HAD RECEIVED A WEATHER BRIEFING THAT REPORTED CEILINGS AND VISIBILITIES AT OR BELOW INSTRUMENT APPROACH MINIMUMS IN THE VICINITY OF HIS DESTINATION AND FORECASTED AND REPORTED AIRFRAME ICING ALONG HIS FLTROUTE. THE PILOT FILED AN IFR FLT PLAN. AFTER THE ACCIDENT HE STATED THAT HIS PASSENGER WAS EAGER TO GET TO NEVADA FOR AN APPOINTMENT ON 4/9/83. USING THE FUEL CONSUMPTION CALCULATED FROM THE LAST FLT THE ACFTS FUEL RANGE WAS ABOUT 4 HOURSTHE FUEL WAS EXHAUSTED AFTER 4 HOURS AND 15 MINUTES ON THE ACCIDENT FLT.