The pilot stated that the airplane encountered a downdraft while on short final to runway 19 at Big Creek, Idaho, which resulted in a sudden drop from about 15 feet, and subsequent hard landing. The landing bent the nose gear forward and damaged the firewall. The Big Creek Airport is a remote mountain airport with a turf runway. The pilot made a field repair by lashing the nose wheel strut back using rope and a come-along attached to the main landing gear. The pilot then proceeded to fly the airplane to McCall, Idaho, about 30 minutes away, where an mechanic assessed the damage and advised the pilot not to continue the flight. The pilot decided to continue the flight to his home base, Minden-Tahoe Airport, Nevada, approximately 454 miles southwest of McCall. The elevation of the Big Creek Airport is 5,743 feet mean sea level. The pilot reported the outside air temperature at the time of the accident to be 80 degrees Fahrenheit (26.6 degrees Centigrade). At 1350, the McCall Airport weather observation was winds from 210 degrees at 11 knots; 8 statute miles visibility; temperature 26 Centigrade; dew point 5 degrees Centigrade; and the altimeter setting was 30.05 inches of mercury. The calculated density altitude for these conditions at Big Creek is 8,238 feet mean sea level.