Yes, sunscreen is important even in the winter and on cloudy days. The sun is shining on your skin when you go outside, regardless of the temperature, so use sunscreen.
It's absolutely worth it to use sunscreen in winter. Ideally, use sunscreen every day. The sun's rays are actually stronger in the winter, so risk of sun damage is greater.
Yes, you should use sunscreen in the winter. Even though the sun's rays are weaker in winter, they still cause skin damage. Sun damage is cumulative over a lifetime.
Yes, the sunscreen can be used even in the winter and it is really worth to use the same especially when going out in the open under the sun or when having sunbath.