Hi
Welcome to the MedHelp forum!
Yes cold weather can make the elbows dry red chaffed and itchy too. Apply a good moisturizer sever times a day. Glycerin mixed with rose water too helps.
If this does not help, consult a skin specialist for it could also be due to eczema, dermatitis or fungal infection.
Hope this helps. Please let me know if there is any thing else and do keep me posted. Take care!
Cold weather can make em red, not sure if they can make em feel like burning.
Put olive oil on them for the dryness.