No I don't wear sunscreen in winter.
Having had a melanoma on my face, I possibly should but would not think of doing it when it is overcast and not hot.
I walk my dogs every morning and even in summer I do not do it as I figure it is early and the sun will do good at that time.
I was told once that I needed more sun, and I believe that millions of people suffer from a lack of Vitamin D and the best way to get this is in the sun when the sun is not so strong. Otherwise you could end up with osteoporosis so I do not think sunscreen is a good idea in winter.