The uncertificated student pilot stated that he had been watching the weather for three days waiting for suitable flying conditions. He checked the automated weather at a nearby airport, and decided that conditions were suitable for flying. He and a passenger then took off on a cross-country flight. During the climb to cruise altitude, the uncertificated student pilot began to notice specks of ice on the windscreen. A short time later, ice suddenly began to accumulate rapidly on the airplane, obscuring the windscreen. He could see an airstrip ahead and to the left of the airplane, and started a rapid descent to set up for a landing. As he approached the airstrip, he said that he was still too fast and too high to attempt a landing, so he initiated a go-around. During the second landing attempt, he said that the airplane felt very heavy and sluggish, and as he began to slowly decrease the throttle on the landing approach, the airplane began to lose altitude very fast. He attempted a second go-around, but the engine backfired and lost power. He landed the airplane just past the end of the airstrip on a dirt road, but the right wing struck a power line guy wire, and the airplane spun to the right, striking a road sign. The airplane sustained substantial damage to the right wing and empennage. The pilot stated that there were no preaccident mechanical anomalies with the airplane that would have precluded normal operation.