The pilot said while in level cruise on an IFR flight the engine began to loose power due to carburetor ice and attempts to remedy the situation were unsuccessful with the engine eventually loosing all power. The pilot declared an emergency with Albuquerque Center and was radar vectored toward the Show Low Airport. The flight was intermittently in clouds during the emergency descent and broke out at a low altitude. The aircraft had insufficient altitude to make the airport and landed in the only available location, a field about 23 miles from the airport. During roll out, the aircraft collided with a ditch and nosed over. Post accident examination of the aircraft by FAA inspectors revealed that the carburetor heat box had separated from the heat muff of the exhaust system and was hanging loose in the cowling attached only by the fabric hose. A metal band which attaches the carb heat box to the muff had separated. Chaffing on the cowling in the area of where the heat box was hanging indicated it had been separated for some time. The last 100 hour inspection was accomplished 80 operating hours prior to the accident.