Hello,
Dry skin results when there is not enough water in the stratum corneum for it to function properly. The mainstay of management is liberal use of moisturizers after washing with luke warm water. Soap should be used minimally. Moisturizers should be reapplied liberally during the day. You can also use a topical cortisone (steroid) cream or ointment like dermacort(hydrocortisone). Adding a humidifier to the central heating system of your home or using a humidifier also helps.
If still the symptoms persist then possibility of eczema or atopic dermatitis is there. Please consult a dermatologist for clinical examination in that case as treatment is specific for each one and without clinical examination, it is difficult to make a diagnosis.
I hope it helps. Take care and please do keep me posted in case you have any additional doubts. Kind regards.