Brief Answer:
Moisturizer+
Topical Steroid (mix 1:1 and apply)
Detailed Answer:
Hi. Thanks for posting your concern at HCM.
I am Dr. Kakkar. I have gone through your concern and I have understood it.
I would keep a possibility of Chronic cummulative irritant 
contact dermatitis.
But, I would like to gather some more information from you in order to help you better.
--Does she has any symptom like itching or pain at the site of lesion?
--Does she engage herself in routine household work which requires prolonged contact with water, soaps, detergents, cleansers etc
Extreme dryness can lead to chapping and cracking/fissuring of the skin of hands and feet. People who are atopic/allergic have a low water retentive capacity of the skin, which leads to increased trans-epidermal water loss into the atmosphere specially when the weather is dry and 
cold in winters. 
Repeated washing with soaps exacerbates the condition leading to painful cracks and fissures.
In such a situation it is advisable to apply a good moisturizer as frequently as possible. Moisturizers specially those which contain hygroscopic (attract water from the atmosphere and lock it into the skin) and keratoloytic agents like 
Ammonium lactate, Urea, Lactic acid and 
Glycerin and 
Hyaluronic acid are specially useful in such cases.
Moisturizers should be applied as frequently as possible, and each time after washing hands with soap.
I usually ask my patients who are severely affected by dry, scaly and cracked skin to mix (in equal proportions, 1:1) a potent topical steroid like 
clobetasol cream and moisturizer and apply at least twice daily.
Once the condition improves with this combination, usually within 2-4 weeks, only moisturizers alone would suffice.
regards