A Cessna 172M experienced a loss of power and collided with rough terrain on landing. The pilot indicated he was cruising at 9,500 feet MSL (1,500 to 2,000 feet AGL) with an OAT of 40 degrees Fahrenheit. The carb heat handle was in the 'off' position when the engine began to run rough. He then pulled the carb heat handle out (on) and the engine ran rougher. The carb heat was pushed in (off) and the engine continued to run rough and eventually quit. The aircraft was being operated in conditions prevalent to fuel vaporization ice in the induction system. A weather observation facility located 45NM to the NW reported a temperature-dewpoint spread of 25 degrees which relates to a relative humidity of approximately 40% and in the potential area for carb ice. The aircraft flight manual states, 'To clear the ice, apply full throttle and pull the carb heat knob full out until the engine runs smoothly; and then remove carb heat and readjust the throttle.'