You should apply sunscreen to all exposed areas of the skin all year long. Although it is true that you receive less sun in the winter, your face and hands are exposed to sun all year. During winter months when daylight hours are shorter, the sun hits the earth at a different angle and most of us are wearing more clothing because it is cooler, so you may not think you need sun protection, but your skin is still exposed to harmful rays, even through window glass.
People who don’t wear sunscreen year-round are more susceptible to the development of brown spots on their hands and face (especially the left side, which is exposed to more sunlight through the driver’s-side car window). They are also more likely to develop red crusted spots (actinic keratoses), which can turn into skin cancers. So my advice is to wear sunscreen all year long — even during winter when you think you may not need it.