BE58 PLT HAS RWY EXCURSION ON LNDG AT ZZZ.

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AT 6000 FT MSL; OAT -18 C; IN AND OUT OF THE CLOUDS. THE FORECAST WAS FOR ALTERNATE IFR AND MVFR IN ZZZ WITH SURFACE TEMPS -10 C AND BELOW; AND NUMEROUS PIREPS OF ICE ABOVE 10000 FT MSL. APPROX 50 MI FROM ZZZ; I BEGAN TO PICK UP LIGHT RIME ICE ON THE WINGS AND WINDSHIELD. I HAD TURNED ON ALL ANTI-ICE SYS BEFORE TKOF FROM ALB; AND HAD LEFT THEM ON FOR THE DURATION OF THE FLT. HOWEVER; THE TEMP WAS SO COLD THAT THE WINDSHIELD DEICE WAS UNABLE TO REMOVE THE ACCUMULATION. THE ICE WAS VERY SMOOTH; I ONLY LOST 5 KTS OF AIRSPD; UNTIL I POPPED THE BOOTS. AT THAT POINT; ABOUT HALF THE ICE ON THE WINGS SHED; AND THE OTHER HALF DROPPED MY AIRSPD ANOTHER 10 KTS. I WAS STILL GETTING 170 KIAS; MAINTAINING ALT AND CTL WAS NEVER A PROB. 5 MINS LATER; I RPTED THAT THE ICE WAS NOW MODERATE; AND ATC GAVE ME A DSCNT TO 4000 FT. I WAS VMC AT 4000 FT; AND WAS HANDED OFF TO APCH ABOUT 30 MI OUT. ON THE INITIAL CONTACT APCH ADVISED ME OF LIGHT TO MODERATE RIME IN THE AREA; AND I SOON RE-ENTERED THE CLOUDS AND STARTED PICKING UP ICE AGAIN. THE ZZZ ATIS WAS RPTING CEILINGS ABOUT 1000 FT; WITH THE RWY 5 ILS IN USE. APPROX 15 MI FROM THE OM; I NOTICED THAT MY WINDSHIELD WAS NOW COMPLETELY FROZEN OVER. I VERIFIED THAT THE COMPASS WAS SWINGING; INDICATING PROPER OP OF THE WINDSHIELD DEICE; BOTH DURING THE PREFLT AND INFLT; BUT THE SYS HAD BEEN UNABLE TO PREVENT THE ACCUMULATION AND THERE WAS NO VISIBLE INDICATION THAT THE ICE WAS MELTING AT ALL. GIVEN THE TEMP; I FELT THAT THE ICE WASN'T GOING TO MELT EVEN IF I GOT OUT OF THE CLOUDS; AND SO CHOSE TO CONTINUE. WHEN I CHKED WITH TWR; THEY RPTED WINDS OF 310 DEGS AT 5 KNOTS; BUT I DID NOT NEED ANY XWIND CORRECTION ON THE APCH OR LNDG. I FLEW THE ILS VERY SLOW AND STABLE; AND BROKE OUT ABOUT 1000 FT; WITH 10 MI VISIBILITY. I KICKED THE RUDDER MOMENTARILY; AND IMMEDIATELY PICKED UP THE FIELD VISUALLY OUT THE SIDE WINDOW. I STAYED ON THE ILS UNTIL OVER THE RWY WITH NO PROBS; BUT THEN TRIED TO GO VISUAL USING THE VIEW OUT THE SIDE; AND DRIFTED TO THE L. I TOUCHED DOWN WITH THE L WHEEL JUST OFF THE RWY; AND HIT AN EDGE LIGHT WITH THE PROP. THE GND WAS FROZEN HARD; SO I HAD NO DIFFICULTY IN STEERING BACK ONTO THE RWY ONCE I REALIZED WHERE I WAS. IN RETROSPECT; I SHOULD HAVE STAYED ON THE ILS ALL THE WAY TO THE GND; OR AT LEAST DEVOTED THE BULK OF MY ATTN TO THE LOC WITH A QUICK PEEK OUT THE SIDE TO SEE WHEN TO FLARE. IN A SCENARIO WHERE AN ILS IS NOT AVAILABLE; I WONDER IF IT WOULD BE EASIER TO LAND VISUALLY ON A RWY WITH ONLY EDGE LIGHTS? RWY 5 AT ZZZ HAS EDGE; CTRLINE; AND TOUCHDOWN ZONE LIGHTING. WHILE THAT IS CERTAINLY VERY NICE FOR A LOW VISIBILITY APCH; I THINK IT DID NOT HELP IN THIS CASE; BECAUSE I TRIED TO LINE UP ON THE CTRLINE; BUT THERE WERE TOO MANY LINES OF LIGHTS; AND SOMEHOW I LINED UP ON THE EDGE LIGHTS INSTEAD. IN THE FUTURE; I WILL ALSO CONSIDER RADICAL ACTION TO AVOID ICE IN VERY COLD CONDITIONS.