I don't feel the eye make up is overkill given the area they live in.
It actually helps with some glare and with your vision while you are riding a horse over those kinds of lands.
But if you are American, the only thing I can point to you can relate to are helmets and stickers or cheek make up on Football players. They have these things in part to cut down on glare and improve vision. They aren't even on top of horses traveling across plains and they still have some anti-glare things.
Remember they are baseing clothes, make up, and hairstyle on a compliation of peoples in reality.
That style of Make Up was popular in Asian, The Middle East, and North & North Eastern Africa. Especially in Plains and Deserts. So I don't find it at all strange they'd give him make up like this.
I do believe we also end up with lighting issues and his brow and eyebrows end up casting so much shadow that you might believe they put solid black make up on him as eyeshadow ( too much and too far out over and beyond all his eyelid, all the way to his eyebrow). That doesn't help things. It can some times destroy or distract from the work they did do on his eyes and eyebrows. But nothing can be done about it.
I did not like their wedding night scene in the show, they made it look as if he were forcing her.
In the book, she was willing and he was so sweet to her. It's probably the most romantic GRRM will ever get haha.
I doubt he was that nice to his "spoils of war" though gonk
Of all the images to stop working... it's one where he is in good lighting, moving around ( Animated Gif), where you can see he doesn't have as much Eyeshadow as it appears but his brow is so large is cast shadow there.
As for how nasty and savage they make them, I actually like that. It creates a hard contrast. Dany is going from a little palace she has been sheltered in into the worst savages in the world. Yet,.. the worst people on Earth are still better then her Brother.