The pilot reported that, he checked the airport’s wind indicators while on final approach prior to landing. He observed the wind tee to his left, which was partially obstructed by buildings, indicate a left crosswind, while the windsock to his right, abeam the runway numbers, indicated a right crosswind. He landed the airplane with 20° of wing flaps extended at 75 mph and subsequently retracted the flaps after the main landing gear touched down. According to the pilot, at that moment the airplane was impacted by simultaneous wind gusts from the left and right, and the prevailing wind pushed the airplane to the left. The airplane departed the left side of the runway, the nose landing gear collapsed, and the airplane dug into soft dirt, which resulted in substantial damage to the left wing. The pilot reported no preaccident mechanical failures or malfunctions that would have precluded normal operation.