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I choose Option 2. I don't want to risk falling through the ice as my partner did (Option 1), and I don't want to leave my partner there alone (Option 3), as it's highly unlikely they'll be able to get out without help.

If I lie down, the pressure per square foot on the ice will be minimal, so it's highly unlikely that the ice will break under me. I will be able to help my partner out of the water, probably in a minute or so.

(Note – If I happen to see any long thick branch lying around, I might grab that, and stick it out for my friend to grab onto.)

Once my partner is out, we'd strip off their clothes, which would turn to ice in a few minutes if we didn't, and hang them near the fire. I'd give my partner some of my clothing, then cover them in the aluminum foil blanket. Then I'd get the fire roaring, and dry the clothes.

I would definitely pick this option. Jut as your partner didn't know they were standing on a body of water, you don't know where the water body begins or ends. Being on your belly helps spread the weight instead of focusing it on one point and risking breaking the ice and falling into the water yourself.

Having taken them out of the water, I'd get us back to the fire, get naked (because their clothes are completely wet, possibly frozen, and I just got on my belly on snow, so mine must be damp as well), get under the thermal blanket I think we have and simply sharing body heat by the fire until our clothes are dry (thanks again, fire) and we may proceed.

Yay for flammable tortilla chips ;)

Once they are out and both are safely off of the ice, it's time to get the wet clothes off of your partner. Give them some of your clothes and head back to the fire. Tell them that they aren't allowed to go off alone anymore since the world seems to have it out for them.

LOL!

But... most accidents happen at home...

;)

Very true!

I choose 2

Yay for flammable tortilla chips ;)

Lol, rinse and repeat for me :-) I wrote why in my previous comment :-)

I choose this because I have to be very careful not to break more ice. Sitting on the edge will put too much weight on just one portion of the ice, hence I might fall as well. But if I crawl towards the edge, my weight would spread out and it will be easier for me to pull him out.

Once he's out of the water, I'd strip him off his wet clothes, wrap him with the emergency blanket and make him sit beside the fire while telling him "OMG you're so stupid." Lol. That's all, thank you. :)

I choose option 2. This is the best one as we have to be careful not to break more ice near the edge. Crawling on the belly will increase the area of contact with ice and thus distribute the body weight to a larger area.

Zombie

Having been dead for a few hours, now, I’m not sure wether my body weight has changed significantly, but I guess my internal organs haven’t had time to decompose, yet, so I’m still pretty much what I was. Therefore crawling is preferable to standing on the edge on my two feet.
The good news? I’m dead, so the cold won’t bother me, anyways cue cape toss

Once my partner is safely out of the water, his wet clothes need to come off at once. If I were alive, I’d go skin to skin under the blanket right away, but since whatever body heat I might have retained in death was used earlier to warm up his hands, it’s probably better if I give him some of my dry layers of clothing, sushi him inside the blanket (hosomaki style), and get the fire roaring.
As he warms up by the fire, dry clothes and blanket around him, I’d busy myself with creating a shelter for the night.

This option. Staying low on the ice helps keep it together. Once out, get my partner out of their clothes and into the emergency blanket.

I thint option 2 is the safest way.
After I pull my partner out, I'll check if he's breathing. Maybe he will needs in artificial respiration. After that, it is necessary to remove all wet clothes from him, give something from your own dry clothes and wrap it in a blanket. His clothes can be dried near the fire

This is what I would do though I am a zombie

dead
to avoid breaking the ice further, I would move on my belly towards my partner putting as little strain on the frail ice layer as possible.
After she is out I will have to get her naked to prevent the clothes from drawing too much of her body heat. Then quickly wrap her in a blanket. This should happen where there is as little wind as possible.

Brrr, I'm cold just thinking about it.^^

To be honest, there are aspects of each scenario I like, but getting flat and spreading my weight is the primary concern, so option 2 it is. I would ideally also use my belt to give her something to more easily grasp as in scenario 1, and I would also advise her to swim to the edge of the hole to try breaking away the thin ice where she fell in until she could find a better purchase on the edge, but especially in this case, she is likely panicked and not open to helpful advice.

Once out, since you didn't say we are near the fire, we need to get her to the fire and get her out of the wet clothing. I would use the emergency blanket as a reflector with her between it and the fire to be warmed on both sides. Then, the next priority is hanging the wet clothing to dry.

option 2, but the reality is that you should still use your belt. the ice is obviously thin where your partner fell! so you want to stay as far as you can from it AND reduce your load per unit area!