All correct and very informative answers..
Thank you Goldenrivett, as you pointed out, the only reference to the use of engine anti-ice when SAT is below -40 degrees is in the Airbus "getting to grips with COLD WEATHER OPERATIONS"
When you are crossing the Equator in an area of high MORA at FL380 in cloud through a line of embedded CBs with tops up to FL520 in heavy precipitation and a SAT of -44 degrees, knowledge and common sense must prevail.
The -40 degree limit for using engine anti-ice in cruise is chosen "because practically no supercooled water might be present at colder temperatures" (reference from the same manual)