Actually now you don't see the snow, so I would have to say not.
And this is apparently one of those moments when an artist's instinct works better than the patron's request. With lighter hair, the avatar looks almost like a wight, or at least like he's some manner of intelligent undead. Maybe the last one would work, if you switch the snow line back to black. Other than that, the originals work the best. Thank you for the effort, though. Switching avatars now...
And as promised, here's one internet for your trouble. Don't spend it all at once
*Calculates time for re-colourings*
If I'm generous it was 5 minutes work, upload and post included.