THE STUDENT PLT DEPARTED DEXTER, MO AT APRX DUSK ON A VFR, NO-FLT-PLAN FLT TO HOUSTON, MO. TIME REQUIRED FOR THE FLT WOULD HAVE BEEN APRX 30 MIN (ESTIMATED). AT 1900 CST, THE BUNKER, MO CITY MARSHAL REPORTED THAT AN ACFT FLEW OVER BUNKER SO LOW THAT HE THOUGHT IT WOULD HIT THE WATER TOWER. APRX 1/2 HR LATER, ANOTHER PERSON REPORTED A LOW FLYING PLANE OVER HIGHWAY 72 NEAR BUNKER. NEAR THE SAME TIME, CAMPERS BETWEEN BUNKER & SALEM, MO SAW A LOW FLYING PLANE CIRCLE AT ABOUT TREE TOP LEVEL, THEN DEPART TO THE NORTHWEST. SHORTLY THEREAFTER, THEY HEARD A POPPING SOUND & THE THE ENG NOISE QUIT ABRUPTLY. THE ACFT WAS FOUND THE NEXT DAY WHERE IT HAD IMPACTED WITH TREES APRX 30 FT AGL, THEN CAME TO REST AT THE BASES OF 2 LARGE TREES. AN INVESTIGATION REVEALED THERE WERE AREAS OF IMC ALONG THE ROUTES & THE PLT HAD BEEN CAUTIONED THAT VFR FLT WAS NOT RECOMMENDED. THE SEARCH FOR THE ACFT HAD BEEN DELAYED DUE TO DARKNESS & THUNDERSTORM ACTIVITY. AN EXAM OF THE WRECKAGE REVEALED NO EVIDENCE OF A PREIMPACT, MECHANICAL FAILURE.