IIRC there are products to slather onto exposed skin and protect against frostbite.
Vaseline.
http://warmskin.com/warmskin.html
Warm Skin® warms by holding in
the body’s own natural warmth and serves as a barrier to prevent water loss.
Warm Skin® also moisturizes the
skin to keep it comfortable, pliable
and healthy even in the harshest environments.
The worst thing they could do in that weather is to get sweaty. Better to feel a little cold than to get the body wet and risk hypothermia.