During a local flight, the pilot elected to fly into the mouth of Peter's Creek Valley to look at a friend's cabin. He stated that after he flew over the cabin at about 1500 ft MSL, he "initiated power and a 180 deg turn." He stated that on application of full power, the engine did not respond in any way. Anticipating a carburetor ice problem, he applied carburetor heat. He stated there was no change in power after this step, so he elected to exchange altitude for airspeed to again initiate a 180 deg turn out of the valley. Also, he stated power was consistently decreasing along with a safe area to make a turn. Subsequently, he elected to land in the best area available which was a fairly flat knoll on the side of the valley. During touchdown, the plane impacted in a nose high attitude at an elevation of about 2000 ft. No preimpact malfunction or failure was identified. The temp & dew point were 45 & 35 deg. Icing probability charts indicated serious carb icing could occur at or below cruise power.