In winter, cold winds and indoor heating can easily dry out and irritate the skin. Therefore, I feel it's important to be a little more gentle than usual when washing your face. When washing, use lukewarm water rather than hot water to reduce skin irritation, and gently rinse rather than rub. After washing, apply a moisturizing product immediately before your skin feels tight to help lock in the moisture.
In winter, rather than simply replenishing moisture, it's much more comfortable to replenish moisture and then apply a protective cream to create a barrier. Because indoor air can be quite dry, it's important to use a humidifier or drink plenty of water to keep your skin hydrated from within. UV rays continue to affect your skin even in winter, so it's a good idea to apply sunscreen before going outside. Focusing on soothing and moisturizing, allowing your skin to rest, rather than over-exfoliating, seems to be the best way to protect your skin in winter.