I've not seen Game of Thrones - interested in doing so but never been in the right place at the right time to catch any of it
For
White Walkers I would undercoat white, then probably go with a very light black wash, then when dry a very light blue wash - possibly with some drybrushing in white over the top since you want a quite messy/furry look. Might then, depending on how it looked, hit it again with a very, very light blue or black wash just to tie the drybrushing back in to the rest of the model again. Edit: Having looked at your image above they look less blue than in my picture, so would probably hit it with black rather than blue.
The eyes I would hit the entire eye socket with a slightly heavier blue wash, then when dry hit the eyes with a blue ink (as it has a gloss finish). I then might get a really, really, really, watered down drop of white paint (basically a white wash

) and then hit the eyes again so you get a nice white rim around the eyeball itself.
For the frost giant skin I would go with what I did for the fatty zombie above - a light black wash, then a regular strength (possibly slightly watered down to be on the safe side) blue wash (can always make it darker with another wash over the top!).
You can add things like tattoos easily by pre-painting them before washing - gives the added bonus of not having to strip and redo lots of work if you mess it up.
Example:
The barbarian on the right had a blue wash applied over a white undercoat and then sepia added for the skin. The barbarian on the left had the same except with a red ink (as red washes tend to be too wishy washy for bright colours - inks are much better for this and putting another wash over the top kills the gloss).
If you want to have a look at some other stuff I have done, check out
my PLog - need to update it as I did some painting over the last couple of weekends while I was home