The pilot of an airplane not equipped with radios or certified for flight into instrument meteorological conditions reported that during the initial climb, "I was in the fog and knew I had to get back down." The pilot further reported that he navigated the airplane to two other nearby airports with a non-aviation handheld global positioning system, but both airports were fogged in. After flying for about 30 minutes, the pilot reported that he was concerned with the fuel remaining, due to only taking off with about ½ full fuel tanks. He subsequently navigated back to the departure airport and saw the grass runway below him through a hole in the fog. The pilot reported that he "slipped it through" the hole, but his touchdown was about ¾ of the way down the wet grass runway. The pilot attempted to ground loop the airplane within the runway distance remaining, but the airplane continued straight and overran the runway, impacting a ditch and vegetation. The fuselage and both wings sustained substantial damage. The pilot did not report any mechanical malfunctions or failures with the airplane that would have precluded normal operation. The pilot reported that he did not obtain a weather briefing prior to flight. He also reported that during preflight he observed "a little fog sneaking up over a nearby hill." The departure airport was not equipped with an automated weather observing station (AWOS), but an airport with an AWOS 10 nautical miles southwest at the time of departure reported the visibility at ¼ statute miles with fog, a cloud ceiling of 100 feet overcast, and a temperature of 68 degrees Fahrenheit (20 Celsius) and dew point of 68 degrees Fahrenheit (20 Celsius). The Federal Aviation Administration Pilot's Handbook of Aeronautical Knowledge (PHAK) in part states: "When the temperature of the air is reduced to the dew point, the air is completely saturated and moisture begins to condense out of the air in the form of fog, dew, frost, clouds, rain, or snow."