You wouldn't normally wear a compression shirt on its own if you were training outside. It's all about the layering - so you have a compression shirt that would

You wouldn't normally wear a compression shirt on its own if you were training outside. It's all about the layering - so you have a compression shirt that would wick moisture away, a mid-layer of variable material depending upon the temperature, and a 'shell' outer layer (also breathable). The outer-layer helps prevent wind-chill and water getting in, the mid-layer insulates you, and the inner compression layer wicks the moisture away and keeps you comfortable. Of course, different strokes for different folks, and some people feel the cold more than others!