C182 PLT EXPERIENCES GS FAILURE; SEVERE ICING; AND EXCURSION BELOW MINIMUM ALT ON APCHS TO SFF.

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VECTORS WERE GIVEN TO INTERCEPT THE ILS/DME RWY 21R APCH FOR LNDG AT SPOKANE FELTS FIELD. UPON NEARING THE FINAL APCH COURSE; A FAILURE OF THE GS OCCURRED. I CALLED A MISSED APCH AND VECTORS AND ALTS WERE GIVEN BY APCH CTL. A SMALL AMOUNT OF RIME ICE HAD BUILT ON THE AIRFRAME AT THIS TIME. AFTER EXECUTING THE MISSED APCH AND VERIFYING THAT THE GS INDICATOR WAS INOP; THE VOR RWY 3L APCH WAS ATTEMPTED. THE CTLR GAVE VECTORS TO THE INBOUND VOR COURSE. DURING INTERCEPT OF THE FINAL APCH COURSE; ICE BUILT RAPIDLY ON THE AIRFRAME. AFTER THE REALIZATION OF MODERATE TO SEVERE MIXED ICING DISTRACTED AND ALLOWED THE ACFT TO DSND 400 FT BELOW THE MINIMUM SEGMENT ALT OF 3800 FT MSL. AS A RESULT OF THE ALT EXCURSION AND THE ACCUMULATION OF ICE. I CALLED A MISSED APCH AND REQUESTED VECTORS AND CLB CLRNC TO WARMER VFR CONDITIONS ABOVE 6500 FT TO MELT THE ICE. IT WAS MY IMPRESSION THAT THE ILS/DME RWY 21R APCH REQUIRED THE DME EQUIP ONLY IN THE EVENT THAT THE APCH WAS BEING FLOWN TO LOC MINIMUMS. THE FAILURE OF THE ON BOARD GS INST ULTIMATELY REQUIRED THE USE OF A DME. THE VECTORS AND ALTS GIVEN BY ATC TO INTERCEPT THE ILS WERE GIVEN IN A WAY THAT WAS NOT EXPECTED. I EXPECTED TO INTERCEPT THE ILS AT 6100 FT (AT AZTEM INTXN) AND PROCEED INBOUND. THE FAILED INST AND UNEXPECTED ILS INTERCEPT POS RESULTED IN POOR SITUATIONAL AWARENESS AND CONTRIBUTED GREATLY TO MY STRESS LEVEL. I RECEIVED A STANDARD WX BRIEFING 1 HR PRIOR TO DEP. THE FORECAST WX AT THE DEST INCLUDED AN AIRMET FOR LIGHT RIME ICE IN CLOUDS; TEMP OF +1 C AND AN OVCST LAYER OF 1500 FT AGL WITH TOPS AT 5000 FT MSL. THE TEMPS AT 6500 FT WERE APPROX +2 C. THE CLOUD LAYER WAS FORECAST TO BE 1500 FT THICK. I DETERMINED THAT SUCH WX COULD BE PENETRATED DURING THE APCH TO THE DEST WITH LITTLE ICE ACCUMULATION SINCE THE CLOUD LAYER WAS RELATIVELY THIN; THE TEMPS WERE SLIGHTLY ABOVE FREEZING; AND THE TIME SPENT IN THE CLOUDS WOULD BE MINIMAL. UPON ARR AT THE DEST; THE LAYER THICKNESS HAD INCREASED TO 5000 FT AND THE ICING SIT HAD DETERIORATED. THE FAILURE OF THE GS EQUIP RESULTED IN MORE TIME SPENT IN THE CLOUD LAYER THAN EXPECTED. THE DETERIORATION OF THE ICING CONDITIONS RESULTED IN MORE ICE ACCUMULATION THAN EXPECTED. THE SPOKANE APCH CTLR ADVISED ME OF REGIONAL WX AND PIREPS. BASED ON THAT INFO; I CHOSE TO ATTEMPT THE ILS/DME RWY 21R TO LOC MINIMUMS WITH THE DME INFO FROM BOTH THE APCH CTLR'S RADAR AND THE ONBOARD VFR GPS. THE APCH AND LNDG WERE SUCCESSFULLY EXECUTED. THERE WAS NO ACCUMULATION OF ICE ON THIS APCH. I PUT MYSELF AND MY PAX IN A DANGEROUS SIT; WHICH TESTED THE LIMITS OF MY ABILITY; EXPERIENCE; AND ACFT. I MADE A VERY POOR DECISION TO ATTEMPT THE APCH CONSIDERING THE WX SURROUNDING THE DEST. THE SINGLE BIGGEST FACTOR; FOR WHICH I WAS UNPREPARED; WAS AIRFRAME ICING. AS PLTS; WE ARE TRAINED FOR EQUIP FAILURES; HOWEVER; ICING PRESENTS A SIT FOR WHICH THERE IS LITTLE TRAINING; AND THE ONLY ALTERNATIVE IS AVOIDANCE AND/OR ESCAPE. I PRIDE MYSELF ON MY ABILITY TO ALWAYS 'STAY AHEAD' OF THE ACFT AND TO FLY WITH CONFIDENCE; KNOWLEDGE; AND AS MUCH PRECISION AS POSSIBLE. I AM ASHAMED AND HUMBLED AS A PLT DUE TO THESE RECENT EVENTS. THIS SCARED THE HELL OUT OF ME. IT WILL NEVER HAPPEN AGAIN.