DURING ARRIVAL, THE CREW OF NPA FLT 1802 CONTACTED THE COMPANY WX OBSERVER AT SOLDOTNA WHO ADVISED THE WX WAS: WND CALM,CEILING 600 TO 800 FT, VIS 8 TO 10 MI, NO PRECIP. THEY MADE AN NDB APCH, BUT MISSED THE APCH & REQUESTED ANOTHER APCH. APRX 1 MIN LATER, THE CREW REPORTED THE ACFT HAD ACCUMULATED A HVY LOAD OF ICE. THEY COULD HAVE DIVERTED NEARBY TO KENAIFOR AN ILS APCH, BUT ELECTED TO MAKE A VOR APCH BACK TO SOLDOTNA. WHILE BEING VECTORED, THEY MADE 2 MORE CHECKS WITH THEWX OBSERVER WHO ADVISED THE WX HAD DETERIORATED TO BELOW MINS & RECOMMENDED DIVERTING, BUT THE CREW DID NOT ACKNOWLEDGE.SUBSEQUENTLY, THE ACFT COLLIDED WITH TREES ON HI TERRAIN APRX 1.5 MI SE OF THE ARPT. THERE WAS EVIDENCE THE ACFT WAS CIRCLING WHEN IT CRASHED. CIRCLING WAS NOT AUTHORIZED SOUTH OF RWY 7/25. INV REVEALED RECURRING PRBLMS WITH THE ANTI-ICESYS, ITS 'SINGLE' MODE WAS INOP, 2 DE-ICE BOOTS WERE MISSING FM PROP BLADES. WX STATION LISTED ONLY 1 LGTD MARKER (1/4 MI AWAY) FOR VIS REF; MIN LNDG VIS WAS 1 MI; CEILOMETER WAS INOP. NO FAA INSPN OF WX STATION IN 2 YRS. ICG FORCASTED.