There may be multiple causes, but a common one is that the relative humidity in our houses is lower in winter. When air is heated the total water content stays the same, so the relative humidity drops, unless your heating system adds additional moisture. Try running a humidifier and see if it reduces the problem.

Normally things dry out slower because cold air can hold (and carry away) less water than warm air can.

Warm things, like your skin, dry out faster because they warm up the cold air around themselves, which is holding very little water because of having been cold, and consequently can take in a lot more while being warmed up.

“Dry out” is ambiguous in context; there are at least two major factors involved. In winter skin looks and feels drier than in warm, humid weather, but drying in the sense of losing water is slower in the cold. Mind you, even cold mammals lose water fast, because their bodily heat speeds up evaporation. Still, sweating aside, healthy skin retains water and stays soft because it is impregnated with waxy and fatty substances that keep it flexible and reduce evaporation. Skin damage, such as bad burns that disrupt control of water loss over large areas of the body, kills largely by dehydration.

People react variously to cold, including in their secretion of waxy skin protection. They differ genetically in their skin chemistry and cold affects the texture of their skin lubrication. In some skins the lubrication becomes practically solid or powdery, which may make it harder for the glands to secrete the material and to distribute it as waterproofing throughout the horny surface of the epidermis. Such factors leave dry skin with that brittle, papery feel. That is why the treatment for  “dry” winter skin is not to apply water, but soft, protective oils, usually as emulsions.

Keep soft,

Jon