AN SF340A DURING APCH AT 4500 FT DECLARED AN EMER DUE TO L ENG ANTI-ICE FAIL LIGHT REMAINED ON. PROCS ARE TO REDUCE PWR TILL LIGHT GOES OUT. WHEN PWR REDUCED TO LIGHT OUT PROP WENT TO FEATHER.

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DURING ILS RWY 23 APCH TO ZZZ AT 4500 FT MSL AND APPROX 12 MI TO THE ARPT WE SELECTED ENG ANTI-ICE ON AS WE WERE ABOUT TO ENTER A CLOUD DECK WITH KNOWN ICE. THE R ENG WAS SELECTED FIRST AND THEN THE L ONE. A MASTER CAUTION SOUNDED ADVISING THE CREW THAT BOTH THE R AND L ENG ANTI-ICE HAD FAILED. THE CHKLIST CALLS FOR THE RECYCLING OF THE ANTI-ICE SWITCH WHICH WAS DONE ON BOTH THE R AND L ENGS. THE R ENG WORKED PROPERLY THIS TIME BUT THE L ANTI-ICE LIGHT REMAINED ON. AT THIS POINT THE CHKLIST ADVISES TO REDUCE PWR ON THAT ENG UNTIL THE LIGHT GOES OUT. I REDUCED PWR ON THE L ENG UNTIL THE LIGHT EXTINGUISHED. A MOMENT LATER; THE L PROP FEATHERED. THE CREW DECIDED TO SELECT THE L CONDITION LEVER TO FEATHER AND ALSO TO ADVISE ATC THAT WE WERE DECLARING AN EMER. WE ALSO LEVELED OFF AT THAT POINT TO AVOID FLYING INTO THE ICE UNTIL WE WERE READY TO CONTINUE THE APCH. WE CONTACTED ATC; FLT ATTENDANT; PAX AND COMPANY AND ADVISED OF OUR SIT. WE THEN ELECTED TO CONTINUE THE APCH WITH THE L ENG IN FEATHER IN CASE SOMETHING HAD BEEN DAMAGED. WE ADVISED ATC AND THEY VECTORED US FOR THE ILS RWY 23 AND WE LANDED WITH NO FURTHER INCIDENT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE CAUSE OF THE PROP GOING TO FEATHER WAS A PROCEDURAL ERROR IN REDUCING THE PWR SLIGHTLY BEYOND THE POINT WHERE THE ANTI-ICE LIGHT WENT OUT. THE AIRPLANE GND CHKED OK BY MAINT ON BOTH THE ANTI-ICE LIGHT AND THE AUTO FEATHER SYS.