On June 6, 1994, at 0240 central daylight time, a Cessna 182, N5380N, registered to Skyhawk Flying Club, Inc., and flown by a private instrument rated pilot, nosed over during a landing roll at the Millard Airport, Omaha, Nebraska, while on a personal flight. Visual meteorological conditions were reported and no flight plan was filed. The airplane was substantially damaged. The pilot and passenger were not injured. The accident portion of the flight originated from Chadron, Nebraska, on June 6, 1994, at 0130 cdt. The pilot stated that just prior to touchdown on runway 12 (3,800' x 75'), the airplane entered an area of low lying fog. He stated he lost forward visibility and attempted to abort the landing but the airplane began to veer to the left side of the runway. The airplane traveled off the runway, contacted rough terrain and nosed over. The pilot stated he listened to the Aviation Weather Observation Service (AWOS) report twice while approaching the airport prior to landing. He reported that both times the report stated conditions were clear below 12,000' with 2 1/2 miles visibility, and a low temperature/dewpoint spread.