Well, one of the problems with some of the shots (with characters faces) is lighting. The thing is - it looks the same in most of the games ( like The Last of Us Part II, Uncharted 4, God of War) where you have a weather with clouds and no sun. It means that the scene lighting doesn't have a directional light source only Sky light (HDRI if you like). Because of that you don't have a proper shadows, mostly ambient occlusion.
Overcast sky is hard to make it right because usually it's flat. Everything is lighted the same way because it's this ambient lighting. Even with Ray Tracing it's not much better. What they could do is to make AO maps stronger, so that the holes in the nose would be darkened more, but it would also work for the rest of AO maps so they would need to make some additional lighting layer in renderer.
Anyway this is how lightning in gameplay works. In the cutscenes they could use proper lights to simulate this weather but with ability to fine tune it. But cutscenes are easier to control then the gameplay and have bigger overhead for extra effects.
As I said you can find the same problems in most of the games with this type of weather.