One argument in favour of using sunscreen in winter is that the level of UVA reaching the Earth's surface remains constant throughout the year, whether it be summer or winter, but this appears not to be the case. Apparently, the levels of UVA and UVB exhibit temporal variations over the course of the year, these evidently decrease during the winter months (figure 1). Indeed, the elongated angle and reduced duration of sunlight in non-equatorial regions result in a decrease in UV and their weakening in winter, this is also true for UVA.
Even though exposure to UV and visible light is significantly reduced in non-equatorial regions during winter, the low levels still present can in fact exacerbate photosensitive conditions, such as melanoma, acne andhyperpigmentation. Given that visible light and UV can worsen these issues, it may be wise to use a sunscreen with protection against visible light all year round to prevent pigmentation from darkening.
After taking into account your place of residence, your personal levels of UV exposure, your skin type, and whether you are photosensitive... you can make an informed decision as to whether or not you need a sunscreen in winter. Some will need it, others will not. When in doubt, it may be wise to apply it, just in case, and also to maintain this habit. People inaccurately associate two weather phenomena with UV, namely temperature and cloud cover.