According to the flight instructor, he was simulating an engine failure with the student pilot. He selected a field to approach and proceeded to reduce the engine rpm to simulate the engine failure. They continued the maneuver until they were approximately 100 feet above the ground, at which point he instructed the student pilot to add full power and climb out. The student pilot complied, but right at that moment, the flight instructor felt a heavy gust of wind. He described it as a downdraft, and despite the engine producing full power, it would not climb. The flight instructor took control of the airplane and attempted to recover it from the descent. The airplane continued to descended until it collided with a fence and touched down in the field. During the landing roll, the airplane impacted a tree, resulting in substantial damage to the horizontal stabilizer. The pilots reported that there were no pre-accident mechanical malfunctions or failures with the airplane that would have precluded normal operation. An engine test run was facilitated, and no anomalies were noted during the test.