The reason people usually get itchy skin in the winter is because the weather is cold and dry. The dry air makes your skin dry out causing itchiness and abrasions. Make sure you are getting enough water. if your dehydrated the lips are really dry and chapped and you can do a simple test to see if you are dehydrated other than the lips. Pinch (NOT HARD) a little bit of skin on your hand or arm then let go, if the skin snaps right back then your ok. if it takes a moment then your dehydrated and need fluids ASAP
You should try some calamine lotion to calm your skin, and to keep your skin soft and hydrated try Aveeno. Aveeno has oatmeal in it which is very calming to the skin. Lotions with Shea butter are also great.
if your lips are dry and chapped try applying a little vasline or medicated cream on them after a shower and after a meal. If you do it after a shower it locks that moisture in.
(Martikadragoon, CL Dermatology)
It can be due to dry skin. Too much soapy water, exposure to harsh chemicals, the normal aging process and certain types of skin diseases are some of the causes of decreased amounts of protective skin oils which in turn causes dry skin.
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 or seborrheic dermatitis ruled out. I hope it helps. Take care and regards.