Thank you for your query.
It is unusual to have swollen lips due to cold
weather. It is the fingers of both arms and legs which get affected more because of cold.
If the lips are purple and the finger tips are normal pink in colour then we need not worry as it could follow the swelling described by you. However if the finger tips are also blue then your child needs to be examined by a doctor. As the swelling has gone down and the lips are slightly discoloured then you can wait and observe; it should improve in the next 24-48 hours.
I hope I have answered your query to your satisfaction.
Wishing your child all the best.