I'm having trouble understanding the answers posted above.
I interpreted the OP as a discussion about inlets which are part of the airframe systems.
The engine itself is a separate system. The linkage is the form of water as it enters the engine blading. and into the compressors. at -40C the only engine problem that I am aware in the service experience is that described by tdtracer as ice crystals melting and sticking to internal engine probes only to be shed into the small blading of high speed compressors or the burner itself as a slug of water.
Again I am not aware of any signifcant damage events at -40C having to do with inlet effects on such ice crystals.
If we are talking about icing at conditions above -40C that is another type of discussion as is water ingestion in massive rain storms.