Basically, what Mad Scientist wrote.
Below -40C, it's believed liquid water cannot exist, so what you're dealing with is Ice Crystal Icing (ICI). ICI has caused numerous headaches for engines, where they form ice internal to the engine flow path - forming ice where the temperature in the flow path is well above freezing. In simple terms, what happens is the ice crystals hit a warm surface and melt, additional ice crystals then hit the liquid water and cool it sufficiently that it re-freezes. It builds up then releases all at once - causing compressor damage or quenching the burner (or both).
In the case of inlet anti-ice, the design intent is that the inlet heat will not only melt any ice, it'll evaporate the water so you don't get runback. However below -40C, there may not be enough heat to evaporate the liquid - the danger is the melted crystals flow back and refreeze on the unheated portion of the inlet, then release in big slabs that can cause fan damage.