Extreme changes in temperature and humidity can create havoc with skin. We're used to living in a warm and humid area. Then in the fall and winter we switch to cold, dry air. It's worsened by forced-air heating rather than radiator heat, which provides more moisture. Take a kitchen timer with you into the bathroom, and set it for five to seven minutes.
Some doctors recommend showers over baths because people are less likely to linger in showers.
If you take a bath, use bath oils and moisturizing cleansers. Once a day is enough. In fact, it's the opposite. And keep that water warm, not hot. Hot water feels really wonderful, but it leaves your skin dry as a bone.