This is a concerning symptom. I would recommend that you see your primary care doctor
. If necessary, he or she may refer you to a dermatologist
(a skin and nail specialist) for further evaluation and treatment. Regardless, dry skin patches in these areas require evaluation.
Firstly, dry skin is a common condition medically known as xerosis. This is fairly common, especially in cold climates where the air is more dry. Dry skin is more common on the legs and soles. The face is a relatively uncommon place for standard xerosis. If this is xerosis, then using hydrating creams and lotions is the treatment. These are commonly found over the counter (lubiderm and eucerin and such). That being said, I would first see a doctor to see if this really is dry skin.
Another possibility is that this is another skin condition. Eczema or atopic dermatitis is a common skin condition. This is similar to allergies in the skin and is more common in people with allergies and / or asthma. Other skin condtions such as psoriasis
can also occur. Skin infections (fungal or bacterial) should also be evaluted. These would require other treatments such as steroids or anti-biotics.
Talk to your dermatologist or primary care doctor. This should be evaluated be initiating treatment.