AIR TAXI TURNS OFF RWY GOES INTO LOW SNOW BANK. IT IS ICE UNDERNEATH; NOSEWHEEL COLLAPSES.

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FLT WAS CLRED FOR A VISUAL APCH AND CLRED TO LAND RWY 2L NASHVILLE (BNA). SINCE I HAD TO GO TO THE OLD CARGO RAMP AND FOR TFC REASONS I CHOSE TO EXIT THE RWY AT TXWY A1; THE FIRST TXWY EXIT TO THE L. TURNING TOWARDS THE TXWY; I SAW IN THE SHINE OF THE TAXI LIGHT A SNOW BANK ACROSS THE TXWY. A FEW DAYS BEFORE SNOW HAD FALLEN AND THE SNOW PLOW HAD CLRED ONLY THE RWY. THE SNOW ON THE TXWY WAS ROUGHENED BY CHUNKS OF SNOW THAT THE PLOW HAD THROWN TO THE SIDE. I SLOWED TO SLOW TAXI SPD BUT DECIDED TO KEEP ROLLING TO NOT GET STUCK IN WHAT I THOUGHT WAS SNOW. THE SNOW BANK WAS ABOUT 2 INCHES HIGH AND FLATTENED BY VEHICLES IN MOST PLACES. WHAT I DIDN'T KNOW WAS THAT ALL THE SNOW WAS FROZEN OVER DUE TO FREEZING RAIN THAT HAD FALLEN MAYBE THE DAY BEFORE. SO WHEN THE NOSEWHEEL HIT THE FROZEN OVER SNOW BANK AND THE ROUGH AREA BEHIND THAT; IT COLLAPSED AND THE PROP STRUCK THE PAVEMENT. THE AIRPLANE DID NOT CLR THE RWY AND HAD TO BE CLOSED UNTIL THE PLANE WAS TOWED AWAY ABOUT 2 HRS LATER. THE ACCIDENT HAPPENED DUE TO MY WRONG DECISION TO ATTEMPT TO TAXI ACROSS THE ICE BANK. SINCE MY DEP ARPT (MEM) WAS CLR OF ANY ICE THE DAY OF THE ACCIDENT; I DID NOT EXPECT SNOW OR WORSE - ICE ON THE TXWYS IN NASHVILLE. ALSO I WAS NOT INFORMED ABOUT THE CONDITION OF THE TXWYS; OR MAYBE BETTER CONDITION OF CERTAIN TXWYS. SO INSTEAD OF TRYING TO AVOID IT; I MADE AN ATTEMPT TO GET THROUGH WHAT I ASSUMED WAS ONLY A LITTLE SNOW AND NO MAJOR PROB. A MORE CONSERVATIVE DECISION WOULD HAVE HELPED TO PREVENT THE ACCIDENT. WHEN I ARRIVED AT NASHVILLE THE NEXT DAY; ATC ADVISED PLTS ABOUT THE CONDITIONS ON THE TXWYS AND TXWYS THAT HAD NOT BEEN CLRED WERE CLOSED. THAT; ON THE DAY OF MY INCIDENT; WOULD ALSO HAVE CONTRIBUTED TO AVOIDING THE INCIDENT.