CL65 FLT CREW OVERRIDES DISPATCHER AND DUTY PLT INSTRUCTIONS AND DIVERTS TO ALTERNATE DUE TO RWY CONDITIONS AT LEX.

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I DID A FLT RECENTLY TO ZZZ AND DECIDED NOT TO CONTINUE THE FLT DUE TO UNSAFE RWY CONDITIONS. BEFORE MY FLT; I CALLED MY COMPANY'S DISPATCHER TO INQUIRE ABOUT THE RWY CONDITION UP IN ZZZ. I WAS INFORMED THAT ZZZ RWY WAS CLR AND DRY WITH BRAKING ACTION OF GOOD. ZZZ AT AROUND XA30Z; WAS EXPECTING FREEZING RAIN; SNOW PELLETS; AND ICE PELLETS. I ASKED MY DISPATCHER TO CONTACT ME IF CONDITIONS CHANGED. I DEPARTED TO ZZZ SOON THEREAFTER AND RECEIVED A CALL FROM MY DISPATCHER INFORMING ME OF THE CHANGING CONDITIONS IN ZZZ. RADIO COM WAS EXTREMELY BAD DUE TO THE WX OUTSIDE. I TOOK FROM HIS RPT THAT SNOW PELLETS HAD STARTED TO FALL AND THAT THERE WAS A THIN LAYER OF SNOW AND ICE ON ALL SURFACES INCLUDING TXWYS AND RAMP AREAS. I DECIDED THAT THE RWY CONDITIONS INDICATED A CONDITION OF ICE ON THE RWY. GIVEN THESE CONDITIONS; I DECIDED AFTER LOOKING UP CHARTS FOR ICE COVERED RWY; THAT THE AVAILABLE RWY DISTANCE AND THE REQUIRED RWY DISTANCE; DIDN'T MATCH. IN OTHER WORDS; I ONLY HAD 7001 FT OF RWY IN ZZZ WITH A REQUIRED 8800 FT PER MY CONTAMINATED RWY CHARTS. I INFORMED MY DISPATCHER; BUT HE DISAGREED WITH ME ALONG WITH THE DUTY PLT. THEY SAID IT SHOULD BE CONSIDERED TO BE A DRY RWY. I OVERRODE THEIR DECISION AND RETURNED TO DEP ARPT. IT APPEARS AFTER I LANDED; THAT I DIDN'T GET ALL THE INFO. THE RWY HAD BEEN BRUSHED; BUT I DIDN'T HEAR THAT. REGARDLESS; A PLANE 10 MINS LATER AFTER I DIVERTED; RPTED A BRAKING ACTION OF NIL. BAD RADIO COM AND THE FAILURE OF MY DISPATCHER AND DUTY PLT TO GIVE ME THEIR REASONING BEHIND THEIR DECISION CONTRIBUTED TO THIS ERROR.