Not true at all.
You can get sun damage on windy, cloudy and cool days because sun damage is caused by ultraviolet (UV) light radiation, not temperature. UV radiation penetrates cloud cover and remember it is a light wave – it doesn’t get blown around. Sun damage is also possible on cloudy days, as UV radiation can penetrate some clouds, and may even be more intense due to reflection off the clouds. Most weather apps have a UV forecast that can indicate the true level of UVA and UVB rays on any given day so you can check and this will remind you to put on a broad-spectrum sunscreen.