FLC OF C550; CITATION; ATTEMPTS LNDG AND DISCOVER BRAKING IS INSUFFICIENT AND MAKE A GAR. CAPT BELIEVES HE KNOWS BETTER AND ON SECOND ATTEMPT ACFT GOES OFF THE RWY AND DOWN AND UP A SLIGHT EMBANKMENT; SHEARING THE NOSEWHEEL.

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AFTER SHOOTING THE GPS RWY 27 APCH INTO 3HA; WE WRE IN A SAFE POS TO LAND SO WE EXECUTED A LNDG. UPON APPLICATION OF THE BRAKES I DETERMINED THAT THE RWY WAS SLICK AND THAT INSUFFICIENT BRAKING EXISTED. I CALLED A GAR AND BEGAN TO INCREASE THE PWR. THE CAPT DID NOT BELIEVE THAT BRAKING WAS INSUFFICIENT SO HE TOOK THE CTLS AND APPLIED THE BRAKES HIMSELF. AT THAT POINT HE REALIZED HE WAS WRONG AND REAPPLIED THE PWR TO CONTINUE THE GAR. HE DECIDED THAT HE NEEDED TO SHOOT THE APCH AND LAND HIMSELF SO WE INFORMED ATC OF OUR INTENTIONS. WE WERE VECTORED AROUND AGAIN FOR THE GPS RWY 27 APCH. WHILE ON DOWNWIND TO THE FINAL APCH COURSE; HE DECIDED THAT I SHOULD SHOOT THE APCH AGAIN BECAUSE I DID NOT DO ANYTHING WRONG AND THAT HE WAS WRONG FOR NOT TRUSTING MY ABILITIES AND JUDGEMENT. UPON LNDG THE SECOND TIME; I ONCE AGAIN APPLIED THE BRAKES. THIS TIME IT FELT LIKE THE BRAKING EFFECTIVENESS HAD INCREASED. WE BEGAN TO DECELERATE. APPROX 1/2 WAY DOWN THE RWY; I INFORMED THE CAPT THAT BRAKING EFFECTIVENESS HAD DECREASED. WE DID NOT HAVE ENOUGH ROOM TO STOP BUT WE ALSO DID NOT HAVE ENOUGH ROOM TO GO AROUND AGAIN. THE CAPT THEN SAID HE HAD THE CTLS. HE APPLIED THE BRAKES TO VERIFY THEIR INEFFECTIVENESS. DUE TO A ROAD AND A GUARDRAIL AT THE END OF THE RWY; HE ELECTED TO GO OFF THE L SIDE OF THE RWY INTO A FIELD. AFTER DEPARTING FROM THE RWY THE ACFT WENT DOWN A SMALL EMBANKMENT AND WHILE GOING UP THE OTHER SIDE; THE NOSEWHEEL SHEARED OFF AT THE FORK. THE ACFT THEN CAME TO REST. THE ACFT RECEIVED MINOR DAMAGES AND WE WERE UNHURT. I FEEL THAT THE CONTRIBUTING FACTORS WERE THESE: 1) FAILING TO GET AN UPDATE ON THE RWY CONDITIONS. RAIN WAS PRESENT 40 MINS PRIOR. UPON LNDG IT HAD STARTED TO SNOW AND THE RWY WAS SLUSH COVERED. 2) FAILURE OF THE CAPT TO TRUST HIS FO'S JUDGEMENT AND HIS DECISION TO GAR. 3) MAKING THE DECISION TO EXECUTE A SECOND APCH AND LNDG BY THE CAPT.