Not strictly true A t.
There is plenty of moisture at high altitudes, as anyone who has had to dodge the Cb's over Africa will confirm. Ice can be a problem at any altitude. However, when the temperature is below -40, the super-cooled ice pellets will not stick to the airframe.
The wing anti-ice system on the 747-400 is actually a de-icer. The technique is to allow an appreciable build up of ice to form and then switch it on, so that the ice breaks away in large chunks. The problem with leaving it on for too long is that the melting ice runs back over the top surface of the wing and then freezes, with no way of removing it.
The wing anti-ice system cannot be used when the flaps are extended as the hot air vents to the atmosphere with the leading edge flaps out. The wing anti-ice system only heats the leading edge, and it is the entire wing which required de-icing prior to take-off.
Airclues