Well, the environment we live in has some influence on our appearance I don't believe it has the same amount of influence as suggested in the original post.
If you mean that recent Europeans would move to Asia now and would continue to evolve there, over a long period, they would still look and be different. Some traits may evolve similar to Asians, but adaptation to the present environment would for sure give different results. Besides adaptation, some mutations may happen over time and these are completely unpredictable and not related to the environment. The surviving mutations would be almost certainly be different form the ones that have survived in Asians in the past.
I guess Radrook may be hinting at the idea that some face features evolved as a response to low temperatures. If you compare faces of Asians living far north with faces of Europeans, their ears are shorter and less sticking out and their noses are less pointy. All in all their heads are more spherical. This is evolutionary answer to freezing temperatures - it is less possible to got a frostbite when something is less exposed.