RWY INCURSION DURING REDUCED VISIBILITY CONDITIONS.

Narrative

I WAS PIC ON A DA-50 ACTING AS PF. THE ARPT VISIBILITY WAS RPTED ON ATIS AS 1/8 MI IN FOG. TXWYS AND RWY WERE CONTAMINATED BY SOME LIGHT SLUSH. I WAS HOLDING THE ACFT SHORT OF ACTIVE RWY; COMMUNICATING WITH GND CTL. GND CTLR ISSUED CLRNC TO BACK TAXI ON ACTIVE RWY INTO POS AND HOLD AND CONTACT TWR. WE BACK TAXIED SLOWLY WITH FLAPS UP IN ORDER TO REDUCE THROWING SLUSH UP UNDER THE WINGS AND CONTAMINATING FLAP ACTUATORS. JUST BEFORE THE PNF CHANGED FREQS; I BELIEVED I HEARD THE GND CTLR CLR A BONANZA TO TAXI TO THE END OF THE TXWY IN PREPARATION FOR TKOF. DURING OUR BACK TAXI WE WERE CLRED FOR TKOF BY THE TWR CTLR. WE COMPLETED THE BACK TAXI AND TOOK POS; BUT HAD TO WAIT 30 SECONDS AS THE FLAPS WERE DEPLOYED INTO POS FOR TKOF. JUST AS WE BEGAN THE TKOF ROLL; WE HEARD A NEW CTLR (A MAN'S VOICE HAD REPLACED A WOMEN'S) CLR A BONANZA FOR TKOF. NOT KNOWING WHETHER THIS BONANZA WAS BEHIND US OR ROLLING FROM AN INTXN IN FRONT OF US; I ELECTED TO ABORT THE TKOF. AS WE WERE NOT MOVING RAPIDLY; THE ABORT WAS NOT VIOLENT NOR DID IT REQUIRE EXCESSIVE BRAKING. WE ALERTED THE TWR OF OUR ACTIONS. THE BONANZA WAS INSTRUCTED TO HOLD POS; AND WE BACK TAXIED AND DEPARTED WITHOUT INCIDENT. I FEEL THAT THE CTLR SHIFT AND LACK OF CTLR COORD AND BRIEFING EXACERBATED BY LOW VISIBILITIES AND THE FACT THAT WE WERE BACK TAXIING SLOWLY DUE TO LOW VISIBILITY AND CONTAMINATION CONTRIBUTED TO THE PROB. I WOULD RECOMMEND THAT DURING LOW VISIBILITY OPS; WITHOUT GND RADAR; CTLRS MUST RECEIVE POSITIVE ACKNOWLEDGEMENT THAT A DEPARTING ACFT IS AIRBORNE BEFORE SUBSEQUENT ACFT ARE CLRED INTO POS OR CLRED FOR TKOF.