A good compromise, to ensure that these statuses still matter, would be for it to take your health down to red (possibly flashing red)
In my opinion, this is still enough of a punishment for people to be concerned, but it removes the frustration of dying.
This would still prevent people from running back to their bodies quickly, due to the decreased movement speed.
Other possible additions could be for your stamina to decrease, extra sway whilst aiming, maybe a dry cough when dehydrated. Unconsciousness could also play a part. I think the ‘shaking’ we have when cold should be more intense, too. This would be provide a much richer experience to the survival gameplay, than merely losing health and dying.