We have some descriptions of nomadic peoples.

V century: Attila, Hun ruler, by Jordanes:

He was short of stature, with a broad chest and a large head; his eyes were small, his beard thin and sprinkled with gray; and he had a flat nose and a swarthy complexion, showing the evidences of his origin.

VII century: Tong Yabghu, Khagan of West Turks, by Movses Kaghankatvatsi(I can only find Russian translation of his work: http://www.vehi.net/istoriya/armenia/kagantv/aluank2.html):

They brought a huge pumpkin kangun wide and kangun long and drew the face of the king of the Huns: instead of eyelashes draw lines that could not be seen, a place where should be beard, left disgusting naked, nostrils made 1 span [~20cm] wide, moustache - a rare, so it was easy to recognize him. Then brought [painted] pumpkin, and put on the wall face to him, and, turning to the enemy soldiers, began to shout: "Here he is, your king, come worship him. This is the Jebu Hakan!"

So, as you can see Huns(at least Attila) and people of Turkic khaganate are described as having stereotypical East Asian features. Of course they are exaggerated, but still tell us about their appearance.

However, not all Turkic peoples looked like this. Let's compare description of Yenisei Kirghiz in Chinese sources(excerpt from Tang Shu, in N. V. Kyuner, Chinese sources about the peoples of southern Siberia, Central Asia and the Far East., Moscow 1961):

Their inhabitants are all tall and have large bodies, with red hair, green eyes. Having black hair is conseidered to be unhappy.

Of course here we also could have exaggeration. So as you can see, nomadic Turkic peoples were very diverse.