The pilot stated that there was a crosswind from the left at approximately 9 knots during the landing. After touchdown, the airplane swerved to the left and exited the left side of the runway. The airplane traveled over a grassy median between the runway and a taxiway, and the airplane's nosewheel separated as it traveled over a "dip" in the median. The airplane came to rest upright, and sustained substantial damage to the engine firewall. The pilot reported there were no mechanical malfunctions or anomalies with the airplane. He stated that the airport was surrounded by trees and it was not uncommon to experience "dramatically changing wind conditions" near the runway. During a postaccident examination of the airplane and runway, a Federal Aviation Administration inspector observed skid marks on the runway leading to the grass median, but the pilot could not recall whether he applied brakes during the accident sequence. An examination of the brake system revealed no anomalies.