Is rubbing the body with water and washing the head and feet considered a valid ghusl for janabah when hot water is unavailable?

Wiping a limb with water is not sufficient for purifying from ritual impurity, because washing means making water flow over the limb. If water does not flow over the limb, it is not considered washing, but rather wiping. The prayers performed with this wiping must be repeated, unless you performed tayammum (definition) due to a genuine fear of illness from the cold water, in which case your tayammum and prayers are valid.