The pilot was approaching to land on a private unimproved runway. The field immediately adjacent to the landing area had been recently plowed. The pilot was landing into the direction of the rising sun, which was just coming over the horizon as he was making his approach. The pilot mistakenly identified a plowed portion of the field for the intended landing area and proceeded to land on it. As he touched down, he noticed the landing area was softer than it should have been, so he kept the nose wheel off the ground as long as he could. The nose wheel finally set down in the soft dirt and dug in, resulting in the airplane flipping over on its back. Both of the airplane's wings, vertical stabilizer, and rudder received substantial damage.