After conducting a low pass over the runway to judge the height of the snow, the flight instructor elected to demonstrate a soft field touch-and-go landing. When the airplane touched down, the snow height was greater than he anticipated and the airplane slowed faster than he expected. Full power was applied and the airplane pitched forward. The airplane continued forward on its nose wheel and rolled to the right and left, striking both wings on the ground which substantially damaged both main wing spars. The pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.