Buy a good humidifier and use it when the air is dry. You might use if year round in a dry, arid climate. If you live in a humid climate, you might only need to use it in the winter when your heater is on, pumping out dry, hot air which quickly dries out skin.
If you have to use rubber or latex gloves, put on a pair of thin cotton gloves before you put the rubber or latex gloves on. This will help avoid a reaction to the rubber or latex and will help keep your hands protected from the sweat that these gloves can cause.