I'm not sure, but I thought I saw in a gameplay thing (might be an old leak) a long time ago that a person got a third-person animation were his character was holding his hands together and trying to warm himself. It's definetly left out (if it ever was in, ofc) and looked awesome. Not so sure about the health damage-thing though. I live in Norway (Just think about Skyrim...) and I bicycle to my school every day (even when it's layers of snow outside, like now) and It's not really that cold. (Am I a counted as a Nord with frost ressitance?) Going without any armor or fur on your arms would make it cold, ofc, but that would take a long time to do all those matching armour and freeze ani. things (fur armour = no freeze animation, scale armour = freeze animation, etc.)
Oh, school. Come back when you have done your military service

Myself, I care more about the numbers going on and adequate penalties that makes the game mechanics, rather than animations. If they can slow you down due hypothermia AND slow down the animation, that would be sweet. But having only the animation slow down with no penalty? No thanks.
And just like FONV, I'd like it be to balanced so that it's still a fun game. You knew you had a -2 aiming penalty if you didn't meet the strength requirements for a weapon, but that penalty didn't make the game unbearable.
But ONLY hypothermia? That doesn't make sense. We'd need the whole basic needs thing just like in FONV. So you carry 100+ salt piles and need to get rid of them? Normally you'd just eat them with no penalty at all. In a hardcoe mode, salt would also drive up your thirst (makes sense, right?). Any food that takes salt to it, will also for the same reason drive up your thirst.
My idea around hypothermia revolves around accumulating points depending on climate in the area and sun height. Then multiply the accumulation speed depending on wind factor (wind chill, a real deal), wetness factor (don't swim in cold areas without being prepared), and various insulation factors for various clothing and armor.