Thanks for the information!
The basis of treatment will be, as you have tried, moisturizing the skin and other non-pharmacological measures:
A fragrance-free moisturizer such as Aveeno, Cutibase, Base Glaxal, Cerave and others should be applied as often as needed. The cream should be applied whenever the need to scratch arises, among others.
Personally I recommend a more oily product like Aquaphor, which can protect a bit more. Apply this product before and after every trip, no matter how long it is!
Avoid using soap on your face and, after the bath or shower, avoid rubbing the skin vigorously: instead, lightly pat the skin to leave a thin layer of moisture, then apply the moisturizer or Aquaphor within 5 minutes of getting out of the bath.
Even in milder weather, make sure your child wears gloves and that his or her neck and face are well protected (scarf, neck warmer)
If non-pharmacological measures are insufficient, you should consult a physician for a thorough evaluation of your child's needs.
I hope this has been helpful and remain available if you have any further questions!
Tom Samaha, pharmacist