Itchy skin can have many different causes each with varying treatments and your primary care doctor
can help you differentiate the etiology.
Since the itchy skin occurs mainly during the winter, dry skin (Xerosis) or eczema may be part of the issue. Dry skin can be exacerbated by excessive washing and dry environments. You can try to avoid excess washing and use a mild soap like Dove or Lever 2000. A humidifier (well cleaned) is often helpful during winter months. Moisturizers are extremely beneficial for dry skin.
Eczema, also known as atopic dermatitis, is a condition in which there is a defect in skin molecules that help keep the skin hydrated, such as filaggrin. Eczema often runs in families and can be associated with asthma
and allergies. Symptoms typically get worse during the cold months and can lead to itchy, dry skin. The main aspect of eczema treatment is topical moisturizers. You can moisturize many times a day with fragrant free lotion like aquaphor, vaseline, and hydrolated petrolatum. The thicker the cream/ointment, the better for eczema. In general, ointments are thicker than both lotions and creams.
Contact dermatitis also causes itchy skin and is a reaction to direct skin exposure to an irritant - often metals, detergents with fragrance, toxic plants, and formaldehyde.
Psoriasis is another skin condition that results in itchy skin. It is a chronic disorder that tends to wax and wane. There are various different subtypes but most are characterized by red, itchy plaques usually with small scales.
I strongly advise you to see your primary care doctor in person to evaluate your itchy skin and consider a referral to a dermatologist