The conventional wisdom is that supercooled liquid water - the kind that freezes on impact with the airframe (including the cowl) - cannot physically exist below -40C. Water at such temperatures can exist only as ice, not liquid.
Anti-ice systems don't help at all with ice pellets/crystals - best case scenario, the pellet still bounces off the surface, and goes where it goes (unless there is monstrous amounts of water, also physically impossible at such temperatures, the engine is going to easily cope with the volume of water, since it can cope with thunderstorm levels of rain) - worse case, the heat of the AI system actually causes the ice particle to NOT bounce but instead stick.
The only wrinkle I can think of is that the temperature of the water droplets could be above the "magic" -40C when the air temp is below -40C. (Maybe the supercooled liquid water is rising from a lower, warmer, altitude) In such a case it's conceivable that you could be getting ice accumulation even though the OAt is below -40C. But its a pretty extreme/unusual scenario. (And outside of the, admittedly imperfect, Appendix c icing envelope definition)