Dry white patchy skin can be correlated to eczema and/or psoriasis but also nutrition issues like deficiencies, hydration or gut health issues etc.
So first check your diet, add more vitamin D & omega-3s (from fish) and drink more water diring winter since skin moisture comes from blood.
Second, try to remove gently the dead skin flakes by using a sallicylic acid based cleanser on the area, and then a oil-based cleanser for the rest of the face to not damage skin any further
Third, moisturize with a thin moisturizer gel (night moisturizer?) with aloe vera, hyaluronic acid and glycerin as main ingredients to lock water inside the skin, and then block any further skin water loss with either vaseline or whipped beef tallow
@Spuffy @Randomized Shame @over0