RWY EXCURSION. LNDG OVERSHOT. UNPAVED ARPT. NON TWR ARPT UNICOM.

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I DEPARTED FROM AURORA MUNICIPAL ARPT IN AUG/TUE/93 AT ABOUT XX45 AM FOR BEAVER ISLAND; MI. 6 PERSONS WERE ONBOARD THE ACFT; INCLUDING MYSELF AND 2 CHILDREN. THE ACFT WAS APPROX 100 LBS UNDER GROSS WT AT THE TIME OF DEP. PRIOR TO DEP; I REVIEWED THE RWY LENGTH AT BEAVER ISLAND. THE GUIDE I CHKED LISTED THE WELKE FIELD 9/27 RWY LENGTH AT 2650 FT. THIS IS WELL WITHIN THE LNDG DISTANCE LISTED ON THE SMT'S PERFORMANCE CHART. FURTHER; UPON CHKING WITH THE OPERATORS OF WELKE FILED ON THE TELEPHONE; I WAS ADVISED THAT THE OTHER RWY WAS 3500 FT LONG. TIME ENRTE WAS ABOUT 2 HRS UNDER VFR CONDITIONS. UPON APCHING WELKE FIELD ON BEAVER ISLAND; I OVERFLEW THE FIELD AND CALLED ON THE UNICOM. WHEN I RECEIVED NO ANSWER; I CHKED WITH ZMP TO VERIFY THE FREQ. SINCE NO ONE RESPONDED TO MY CALLS AT WELKE FIELD; I UTILIZED THE WINDSOCK AT THE RWY INTXN TO VERIFY THE WIND DIRECTION. IT SHOWED A XWIND FOR A LNDG ON RWY 9. I FLEW A NORMAL PATTERN AND WAS CONFIGURED FOR A SHORT FINAL WITH FULL FLAPS AT THE SHORT FIELD APCH SPD WHICH IS MY NORMAL PROC. WHEN I TOUCHED DOWN ON THE APCH END OF THE RWY I APPLIED HVY BRAKING. THE BRAKING ACTION WAS ENTIRELY INEFFECTIVE. I CONSIDERED A GAR; BUT AT THAT POINT I DID NOT THINK THAT SUCH A MANEUVER COULD BE SAFELY CONDUCTED. ACCORDINGLY; I FEATHERED THE PROPS AND CUT THE MIXTURES AND MAGNETOS. OBTAINING WHATEVER BRAKING THAT I COULD; I STEERED THE ACFT TO AVOID ALL OBSTACLES. THE ACFT OVERRAN THE RWY BY ABOUT 25 YDS. THE NOSE GEAR COLLAPSED AFTER DIGGING INTO THE SOFT DIRT. AFTER THE ACFT CAME TO A STOP; ALL PAX EXITED THE ACFT IN THE NORMAL WAY. THERE WERE NO INJURIES WHATSOEVER. THE ONLY DAMAGE WAS A COLLAPSED NOSEWHEEL. THE ARPT MGRS HAD TRULY NOT GIVEN AN ACCURATE DESCRIPTION OF RWY CONDITIONS. THIS INCIDENT WAS CAUSED BY AN ARPT MORE INTERESTED IN ATTRACTING TOURISTS RATHER THAN SAFETY.