PART 135 ATX PLT DEPARTED CLRED ALT WITHOUT PROPER CLRNC IN ICING CONDITIONS FROM OFK; NE.

Narrative

AFTER TAKING OFF FROM OFK; I TURNED EBOUND AT ABOUT 2000 FT AGL; I BEGAN TO EXPERIENCE ICE. IN THIS AREA; ZMP APCH CAN ONLY HEAR ME ABOVE 4000 FT MSL (3000 FT AGL). I WAS OPERATING ON A VOID TIME CLRNC; AND I WAS TO 'CHK-IN' WITH ZMP (AT 4000 FT). ALSO; MY COMPANY INFORMED ME THAT I WAS TO FLY TO A DIFFERENT DEST (OTHER THAN FLT PLANNED). AS SOON AS I REACHED 4000 FT MSL; I TRIED TO CONTACT MINNEAPOLIS; THEY WERE VERY BUSY. I WAS IN A BIG HURRY TO CLB BECAUSE OF THE ICE AND I WAS ALSO TRYING TO TELL THEM THAT I NEEDED TO CHANGE MY DEST. WHILE CHKING ON WITH CTR I ALSO ASKED FOR 6000 FT MSL; ALTHOUGH I DIDN'T SAY WHY; I SHOULD HAVE SAID WHY. THE CTLR ASKED ME TO VERIFY REQUESTING 6000 FT. AT THIS POINT; I WAS JUST BELOW 5000 FT MSL AND STILL PICKING UP ICE THROUGH ALL OF THE ANXIETY OF THE ICE AND THE NEED TO CHANGE MY DEST; I DIDN'T REALIZE THAT THE CTLR DID NOT CLR ME TO 6000 FT MSL. AT ABOUT 5600 FT MSL; THE CTLR ASKED ME TO VERIFY 5000 FT. I RESPONDED BY SAYING; 'NEGATIVE; CLBING THROUGH 5600 FT FOR 6000 FT.' CTLR RESPONDED; 'I CLRED YOU TO 5000 FT; YOU'RE NOW CLRED TO 6000 FT.' NOTHING FURTHER ABOUT THE INCIDENT WAS SAID. WHAT I FEEL HAPPENED WAS THAT THE ANXIETY OF ICE (ICING CONDITIONS) CONTRIBUTED TO ME NOT HEARING EXACTLY WHAT THE CTLR SAID) AND/OR THINKING HE ACTUALLY CLRED ME TO 6000 FT MSL. IF I WAS PUT IN THE SAME SIT AGAIN; I WOULD TELL THE CTLR THAT I WAS IN ICING CONDITIONS AND THAT I NEEDED HIGHER. ALSO; I WILL USE AN IDEA THAT A FELLOW PLT TOLD ME THE FOLLOWING NIGHT -- USE THE ADF CARD AS A MAKESHIFT ALT ASSIGNMENT REMINDER.