PLT CREW OF C421 LANDED ON GRASS TO SIDE OF RWY DUE TO WINDSHIELD ICE; OBSCURING FORWARD VISION AT DECISION HT. WINDSHIELD ANTI-ICE SYS APPEARED INOP DESPITE COCKPIT INDICATIONS OF PROPER FUNCTION.

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I WAS SCHEDULED TO FLY 1 PAX FROM ZZZ AND DROP OFF IN OKC. THE WX CONDITIONS AT THE TIME WERE VFR IN BOTH ZZZ AND OKC. DURING MY PREFLT CHK; THE WINDSHIELD HEAT APPEARED TO BE OPERATING CORRECTLY. THE GREEN ANNUNCIATOR LIGHT AND AN INCREASE IN AMPS ON THE AMP GAUGE VERIFIED THIS. DEP FROM ZZZ WAS UNEVENTFUL WITH A TRACE OF ICE ON THE CLB. TOP OF THE CLOUDS WERE APPROX 9000 FT IN THE ZZZ AREA. ARR INTO OKC WAS UNEVENTFUL WITH NEGATIVE ICE ENCOUNTERED AND SURFACE TEMPS ABOVE FREEZING. ON THE RETURN TRIP BACK TO ZZZ IS WHEN THE INCIDENT OCCURRED. DURING MY DSCNT INTO ZZZ; I ENCOUNTERED LIGHT TO MODERATE ICING CONDITIONS FROM 9000 FT AND NOTICED A THIN LAYER OF ICE ON THE WINDSHIELD. THE WINDSHIELD HEAT HAD PREVIOUSLY BEEN ACTIVATED AND APPEARED TO BE WORKING CORRECTLY; HOWEVER; THE ICE ON THE WINDSHIELD TOLD ME IT WAS NOT. AT APPROX 5000 FT; I LEFT THE ICING CONDITIONS AND THE ICE ACCUMULATION WAS APPROX 1/8 INCH ON THE WINDSHIELD; WHICH LEFT ME WITH NO FORWARD VISIBILITY. I CONTINUED A NORMAL ILS APCH TO RWY 3 AT ZZZ. AT APPROX 400 FT ABOVE DECISION HT; I WAS ABLE TO SEE THE SEQUENCE FLASHERS ILLUMINATING THE FRONT OF THE WINDSHIELD. HOWEVER; DUE TO THE ICED OVER WINDSHIELD; I HAD NO FORWARD VISIBILITY. AT DECISION HT; I SAW THE RWY LIGHTS ON THE R SIDE OF THE ACFT. THINKING I WAS ON THE CTR OF THE RWY; I LANDED STRAIGHT AHEAD; ALBEIT WITH EXTREMELY LIMITED FORWARD VISIBILITY. AFTER LNDG IN THE GRASS; I REALIZED THE RWY LIGHTS I SAW OUT OF MY R SIDE WINDOW WERE ACTUALLY THE EDGE LIGHTS FOR THE L SIDE OF THE RWY. I THEN MANEUVERED THAT ACFT BACK ONTO THE RWY. A POSTFLT INSPECTION OF THE ACFT REVEALED NO DAMAGE; AND THIS WAS CONFIRMED THE NEXT DAY BY THE LCL AP'S