A CPR LTT SLID OFF THE SIDE OF THE RWY IN A XWIND. THERE WAS FRESH SNOW ON THE RWY AND THAWING TEMPS.

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ON MAR/WED/93 AT PM30 EST AT TEB; NJ; WHILE ACTING AS COPLT ON AN LTT LNDG AT TEB ON ILS RWY 6; THE ACFT LOST DIRECTIONAL CTL ON AN ICY AND SNOW COVERED RWY AND SKIDDED OFF THE R SIDE OF RWY 6. THE ATIS RPT RECEIVED 15 MINS PRIOR TO LNDG ADVISED OF LIGHT SNOW AND SURFACE WINDS FROM 340 DEGS AT 14 KTS AND A SURFACE TEMP OF 33 DEGS F. THE ATIS RPT DID NOT INCLUDE ANY BRAKING ACTION RPTS. HOWEVER; WHEN ASKED; THE CTL TWR OPERATOR RPTED THE BRAKING TO BE FAIR BUT DID NOT INCLUDE WHAT TYPE OF ACFT HAD MADE THE RPT AND ALSO STATED THE RPT WAS 20 MINS OLD. WITH THE SURFACE TEMP ABOVE FREEZING AND LIGHT SNOW RPTED; I DID NOT EXPECT A SNOW COVERED RWY. I BELIEVE THE SNOW FALL WAS HEAVIER THAN THE RPTED LIGHT SNOW AND FEEL THE CTL TWR HAS A RESPONSIBILITY TO ADVISE ACFT CREWS OF THE ADDITIONAL SNOW ACCUMULATION COVERING THE RWY. THE ILS APCH TO RWY 6 WAS A NORMAL APCH AND LNDG WITH ALL CHKLISTS COMPLETED AND THE AIRPLANE CONFIGURED FOR LNDG. AT TOUCHDOWN THE AIRPLANE HAD NIL BRAKING ON THE SNOW COVERED RWY. THE AIRPLANE CONTINUED TOWARDS THE R SIDE OF THE RWY WHERE THE R SIDE AIRPLANE TIP TANK STRUCK A SNOW BANK NEXT TO THE RWY AND THE AIRPLANE LEFT THE RWY. WX OBTAINED ON THE GND AT MSP AND ENRTE FROM CLEVELAND FLT WATCH DID NOT CALL FOR THE WX WE ENCOUNTERED UPON ARR AT TEB. GND PERSONNEL NEED TO KEEP FLCS ADVISED OF ANY AND ALL CHANGES IN WX CONDITIONS SO THAT THEY CAN EVALUATE THIS INFO AND RESPOND AS NECESSARY WITH ANY CHANGES TO MAINTAIN A SAFE FLT. SUPPLEMENTAL INFO FROM ACN 236654: BEFORE LNDG; THE COPLT ASKED (TWICE) FOR ANY BRAKING ACTION RPTS AND WAS TOLD 'BRAKING ACTION FAIR 20 MINS AGO.' RWY 6 HAD AN ACCUMULATED AMOUNT OF SNOW ON IT. BRAKING ACTION NIL. ALL EFFORTS TO RETURN TO CTRLINE WERE INEFFECTIVE. THE BOTTOM ENTRANCE DOOR COULD NOT OPEN BECAUSE THE L MAIN GEAR COLLAPSED DUE TO EXCESSIVE SIDE LOADS. I ASKED IF ANYONE WAS INJURED AND ALL REPLIED THAT THEY WERE OKAY. THE ACFT CAME TO REST COMPLETELY OFF OF RWY 6; N OF TXWY C; 3500 FT FROM THE END OF RWY 6; WITH 2500 FT OF RWY REMAINING. TEB EMER EQUIP WAS DISPATCHED TO THE SCENE; ALONG WITH AN ARPT AUTHORITY VAN.