I'd be inclined to tone with the carpet, despite you feeling it can be gloomy in the PM.
How about Welcome (Little Greene) or Welcome light which, although grey, has a warm almost pinkish undertone. Think about mirror/mirrors and lighting to brighten the gloom.
Your furniture, if there is any, will also add an element of warmth or make things appear stark/cold depending on what you have... How are the windows dressed? Would you consider bringing in another, warmer, colour into the furnishing?
I would prefer painted walls but am unsure what colour to choose. The hallway has two biggish windows so does get natural light but I am unsure that if we go a bluey shade it would be too cold looking?
I would appreciate any suggestions. Many thanks ESP