The most important factor is insulation, which determines how well the material can keep you warm. Other factors include breathability, durability, and weight.
The best materials for a scarf that offers the highest level of insulation are wool and cashmere. Wool is naturally breathable and warm without being too heavy or bulky. Cashmere is incredibly soft and light while still providing excellent insulation from cold temperatures. Both of these materials can also be easily dyed into beautiful colors that make your scarf look stylish as well as warm.