I think an important consideration of this possibility would be whether the clothes were wet or dry.
Though I only have a general familiarity with the area, in and of itself, my guess is it was not truly hypothermia level cold, even in December and at night.
But, wet clothes can "wick away" body heat very quickly and greatly accelerate hypothermia. Likewise, perhaps alcohol can also accelerate it as well?
Semi desert areas are known for clear skies that don't trap heat. Thus temperatures can fall quickly at night. This could well create a very uncomfortable night for somebody lost and lightly clad.
But... I don't think the cold in and of itself would have been truly debilitating and then become deadly baring any snowballing of compounding circumstances.