The pilot reported that on his second landing he felt a "small" impact just before touchdown, and then the airplane pitched down and skidded to a stop. The pilot further reported that after the airplane came to a stop, he observed smoke coming from the lower left side of the cowling just forward of the firewall. As a result of the post-impact fire that ensued, the airplane was destroyed. The pilot reported that he observed evidence of where the airplane's nose wheel impacted a snow berm located on the approach to the runway. He estimated that the snow berm was about five feet high and about twenty feet wide. The airport manager reported that about four inches of snow accumulated on the ground prior to the accident, but that almost all of the snow had been plowed from the runway. He further reported that the accident airplanes nose gear impacted a snow berm that was about 10 feet off the end of the runway, and about 28 inches high. The pilot reported that there were no preimpact mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation.