Greasy, Grimy, Grima Hair...

[Lalwendë]

At his feet upon the steps sat a wizened figure of a man, with a pale wise face and heavy-lidded eyes.

This all I can find initially about his appearance. It doesn't say anything about him being dark haired so I think they were able to use their imagination a little when casting/dressing Grima. That they chose to have him as a dark haired but pale skinned man plays on established figures of fear in films - the established idea of a hero in a film does not look like Grima (let me pause here and say Hurrah for Tim Burton and Edward Scissorhands... ).

But it is possible that 'book' Grima may have looked like that anyway; perhaps if he was slightly 'different' to the other men in Rohan it might explain why he sought to be a counsellor rather than a horseman. He may not have had the stereotypical appearance or build of a rider. But then I'm not sure the makers of the film would have picked up on that kind of idea.