Turbans reduce damage in sand storms and slow heat gain/loss in the desert. They primarily help in the desert, but they act as weak heat protections in the lava biome (ninja outfit is comparable to diamond protection), and are as warm as earmuffs everywhere else. Although they warm you a little in winter, they do not provide any blizzard protection.
The Ninja Outfit is the second and highest tier of Protection. It can be used for long periods in the Desert. The heat reduction can be seen easily, meaning that you need little Ice Cubes. It requires 1 turban, 6 cord, 4 boar fur, 12 vulture feathers, and 4 penguin feathers. It also needs a workbench near by. This is a hard item to get, as you need to kill boars and vultures to get this item.