Wool is a very bad conductor of heat or it is very good at providing the insulation from temperature. Since Woolen clothes provides a layer of vacuum over the body, the body heat is trapped inside the clothes that is what keeps us warm during winter. Such an idea of conserving and accumulating the body heat during summer would be a terrible idea as we need clothing that helps dissipate the body heat into the atmosphere.
Wool is also hydrophobic which means it repels the water… In such a case, the woolen clothes will not absorb body sweat and help keep the skin dry. On the other hand, cotton absorbs sweat and it dries quickly with outside heat. It is thinner and airy and does not trap body heat inside the clothes, therefore, cotton is preferred during summer or warm weather.