A CL30'S ANTI-ICE SYSTEM FAILED DURING A MISSED APPROACH IN ACTUAL ICING CONDITIONS. UNFAMILIAR WITH SOCAL AREA AND GIVEN A NON-PUBLISHED HOLDING PATTERN THE CREW; NOW IN A VERY HIGH WORKLOAD SITUATION; HAD A TRACK DEVIATION INTO AND OUT OF HOLDING.

Narrative

WHILE PERFORMING THE MISSED APCH ON THE GPS 18 FROM ZZZ ARPT; OUR ACFT ANTI-ICE SYS FAILED; WHILE WE WERE IN ICING CONDITIONS. THE WORKLOAD WAS OBVIOUSLY HVY; AND WE WERE RUNNING CHKLISTS AND COORDINATING WITH ATC FOR A CLOUD FREE ALT AND A SAFE HDG. THE FIRST ISSUE IN COM OCCURS WHEN ATC SENDS US TO ZZZ VOR AND TO HOLD AS PUBLISHED. THE CREW AT THIS POINT IS NOT SHOWING A PUBLISHED HOLD ON ANY OF OUR COCKPIT MATERIALS; AND ATC ONLY KNOWS IT'S A SE HOLD/R TURNS/1 MIN LEGS. THIS WAS NOT A PROB. OUR ISSUE WAS WHEN SOCAL APCH GIVES US A HDG TO INTERCEPT V64 TO TRM VOR. WE ARE UNFAMILIAR WITH THE AREA; AND HAVE NO IDEA WHERE V64 RUNS TO/FROM. THE PROCESS OF FINDING V64 ON THE CHARTS AND SETTING UP THE RADIOS TAKES SEVERAL MINS AND ATC INFORMED US WE JUST FLEW THROUGH V64; AND IF WE WERE NOT ABLE TO NAV AN AIRWAY WE SHOULD HAVE TOLD HIM. I DON'T THINK ATC REALIZES HOW LONG IT TAKES TO FIND AN UNPLANNED AIRWAY AND SET UP THE RADIOS TO INTERCEPT. WE TOLD ATC WE WERE IN CLR CONDITIONS ON TOP; SO TERRAIN AVOIDANCE WAS NOT AN ISSUE. EVEN COMING OUT OF THE PRIOR HOLD COMS WERE POOR. WE WERE CLRED OUT OF THE HOLD; AND THEN TOLD NO; WE NEED YOU IN THE HOLD UNTIL THE SOCAL HDOF. CONTRIBUTING FACTORS -- WHILE OUR SITUATION WAS NOT AN EMER; THE WORKLOAD WAS HIGH; AND COM ON BOTH SIDES WAS POOR. WHILE WE WERE COMMUNICATING OUR ISSUES TO ATC; WE SHOULD HAVE JUST ASKED FOR A HDG ON THEIR CTL; SO ALL WE HAD TO WORRY ABOUT WAS THE ACFT ISSUE/CHKLISTS.