An average person will survive no problems. Your body will wake you during the mild/moderate stages of hypothermia especially as your shivering becomes violent Then the average muppet would get up and walk round to warm up again!

The problem comes with excessive alcohol consumption which means it is possible the body may cool quicker and due to alcohol you may not wake up when a sober person would, meaning you may well stay asleep right until you slip unconcious and eventually die!!!