If your question is why EAI is not required below -40 deg, it has nothing to do with 'saturation'. Conventional icing is related to supercooled liquid water that impacts the cold aircraft surfaces and freezes - and the general belief is that supercooled liquid water can't exist below -40 deg (BTW, -40 C and -40 F are the same temp, so no need to differentiate).
This is not to be confused with "Ice Crystal Icing" - the problem that has been a recent issue for the GEnx engine on the 747-8 and 787. ICI is fundamentally different - when the ice crystals hit a cold surface, they just bounce off and are not a threat. But when the ice crystals hit a warm surface they can melt, additional crystal then cool the water enough that it re-freezes. EAI doesn't help with ICI.