The pilot reported the airplane departed from the airport with a passenger onboard for a local area flight. The pilot maneuvered the airplane for landing on a grass strip, that parallels the asphalt runway. As the airplane descended and turned from base to final, the airplane encountered a “pocket of unstable air” and a “heavy gust” that pushed the right wing up and caused the airplane to rapidly descend. The pilot applied right aileron and full power. The pilot was able to level the airplane; however, it continued to descend. Due to the location of the airplane at the time, the pilot decided to impact the lighted wind cone (a L-807 structure, size 2, located inside of a segmented circle) with the airplane, as opposed to performing an aggressive turn and the right wing impacting the ground. The airplane impacted the wind cone, the wind cone structure collapsed, and the windsock separated from the structure. The airplane came to rest upright on the grass strip. The pilot and the passenger were able to egress from the airplane without further incident. The airplane sustained substantial damage to the fuselage, the right wing, and the right wing strut. The pilot reported there were no preimpact mechanical malfunctions or failures with the airframe or the engine that would have precluded normal operation. A weather study showed that at the time of the accident, a line of cumulus clouds along a convergence zone had passed with a wind shift to the north. This convergence zone likely amplified the turbulence in the low-level boundary layer and resulted in localized gusty winds and convective turbulence. A review of available weather information revealed that the wind shift was not forecasted.