WHILE EN ROUTE TO AUSTIN, TX, THE PLT CHANGED HIS DESTN TO TEMPLE, TX, DUE TO DETERIORATING WX AT AUSTIN. HOWEVER, THE WX AT TEMPLE WAS ALSO DETERIORATING. WHILE DESCENDING TOWARD TEMPLE, HE WAS ADVISED OF A SPL WX OBSERVATION WHICH RPRTD INDEFINITE CEILING 200', SKY OBSCURED, VIS 1/16 MI WITH FOG, WIND FROM 150 DEG AT 7 KTS. THE PLT ELECTED TO FLY AN ILS RWY 15 APCH WHICH HAD MINIMUMS OF 200' CEILING & 1/2 MI VIS. AT 0847 CST, AS THE PLT WAS BEGINNING THE APCH, ANOTHER WX OBSERVATION WAS TAKEN. IT RPRTD AN INDEFINITE CEILING OF 100', VIS 1/16 MI WITH FOG. ACCORDING TO THE PLT, THE FLT WAS NORMAL UNTIL THE MISSED APCH WAS INITIATED, THEN WAS 'SLOW ON GO, HIT TAIL ON PITCH UP.' AT THAT TIME, THE ACFT CONTACTED THE TERRAIN ABOUT 120' SHORT OF THE RWY, DAMAGING THE TAIL CONE & AFT FUSELAGE, BUT THE ACFT CONTD FLYING. THE PLT THEN DIVERTED & LANDED WITHOUT FURTHER INCIDENT AT BROWNWOOD, TX, WHERE VFR CONDS PREVAILED.