There are technical running clothes, which are made with synthetic wicking material like DryFit, Thinsulate, Thermax, CoolMax, polypropylene, or silk options. Avoid cotton clothes because once they get wet, they stay wet.
There’s a big difference between running with cotton socks and those that are made to help to prevent blisters. It is always better if you look for materials such as polyester, acrylic, and CoolMax or Merino if you are running in cold places.
Avoid going out for a run overdressed, once you warm up, your body gets warmer.