In a written statement, the certified flight instructor (CFI) reported that he and his student flew to Byron Airport, Byron, California, to practice landing. They listened to the Byron automatic weather observation service (AWOS), which reported winds from 250 degrees at 9 knots, gusting to 15. They made two successful landings on runway 23. The third approach was made at 65 knots and appeared normal. The approximate time of the third approach was 1130. When the airplane was 50 feet above ground level (agl) and over the runway numbers, the student reduced power to idle per the CFI's instructions. At that moment, the airplane was caught in a downdraft, which abruptly caused the airplane to pitch down and bank to the right. The CFI added full power and applied back pressure on the yoke, but was unable to keep the airplane from descending rapidly. The nose gear and right main landing gear violently struck the runway. The nose gear broke off, and the airplane bounced. The CFI regained control and landed the airplane on both main landing gear while keeping the nose gear off the ground as long as possible. The nose settled on the broken nose gear strut and the airplane stopped on the runway. The CFI indicated that the airplane and engine had no mechanical failures or malfunctions during the flight. At 1100, the Byron AWOS reported winds from 240 at 6 knots. At 1135, it reported winds from 250 at 7 knots gusting to 18.