I've never been hiking in such extreme situations, but if in the situation in the question, i.e. you're hiking in very cold weather and someone falls in (let's say so pretty much their whole body is under, and it's a lake not a river, so no current) what's the best course of action?
Specifically, how do you get them out safely without endangering yourself or others, and what do you do to minimise the risk of hypothermia and other related conditions when they're out?
The guidance given to first responders from the Public Safety Training Academy is as follows:
You try to avoid going in the water yourself unless absolutely necessary, but the 5 options above should all be looked at in order.
pinpoint where the victim is and go for help as in dive in yourself, I suppose? Are there maybe things that you should do prior to dive yourself, such as taking your sleeping bag out of your pack, starting your stove, or any other thing that you'll have trouble doing when you are yourself pretty frozen?
Sirex & Rory have covered getting them out of the water pretty well, but given that getting them out of the water in the first place might be no small feat, you're right in understanding that you're far from out-of-the-woods, so to speak, even after they're out. Getting the victim warmed up is paramount, and their wet clothes are going to be a serious impediment. If there's any way to get them out of their wet clothes and into some dry clothes, that's pretty high on your list. Some possibilities:
The whole idea of changing clothes is that your hiker will be lots more likely to be able to warm himself back up in dry clothes than in wet clothes, so you're looking for any reasonable option to help that happen.
Next, you need to assess your status and consider getting the whole group to safety as soon as possible. If you've been able to get your soggy hiker into some dry clothes (fully or partially), you may be able to just continue your hike. You'll generate some body heat by moving, which will help some. If you have a short distance to travel in order to reach shelter / warmth, this is probably your best bet.
If, however, it's cold enough that you're not going to warm up by hiking, or if you don't have dry clothes, or you had to borrow some clothes from someone (leaving two or more hikers under-dressed) I'd strongly consider getting a fire started in order to warm up and dry off. Some sort of reflective surface (tarp, rock wall, etc.) may help warm you a little more evenly. Dry out your clothes, but don't burn them!
Keep an eye on time vs. your itinerary. If stopping to build a fire will cause you to not be off the trail by nightfall, you'll need to decide if you're staying put overnight or sending someone out for help. All the usual wilderness first-aid guidelines apply here -- don't send anyone anywhere alone, and a group of four is a great deal better than a group of two or three. If you don't have a large enough group to send a capable party for help, I'd be inclined to stay put and keep the group together.
The whole idea here is to keep your head and use the resources of the group to avoid making the situation worse while you're trying to recover.
I've never had this happen fortunately, but I'd imagine it would depend on a few factors. Namely:
How cold the water is.
What gear they are carrying that prevents them swimming?
How muddy the bank / lake bed is - will you get stuck if you enter or approach the water?
I'd personally consider going in after someone just about the last option, and even then only when you've no extra clothing and other ready to aid you leaving the water safely. I believe you can likely be more use from the water edge than in trouble with them, even if its only to grab any wood or such that will float and get it as close to the person as possible to aid in keeping them afloat.
Is there ice? If so, the victim may be nowhere near the edge of the lake itself, and you need to consider how much weight that ice can take.
What do you have available? Assuming there is ice, anything that can spread your weight is useful, as is anything long. Bear in mind many people find gripping difficult in cold water due to shock, but any floatation device or improvised life aid should work.
Best case scenario in my mind is that they pull themselves out the water, either by swimming or by pulling themselves onto the ice and keeping their weight distributed on any ice. At that point you need to go through the steps to increase body core temperature, (by fire, drying clothes, getting out of any wind etc).
It's a pretty complicated question to answer, particularly in a short time span, which I'd imagine goes some way to contribute towards the numbers of people killed in bodies of water each year, and those that die trying to save them.
A couple of additional points which I think have not yet got the attention they deserve.
Time is of the essence. I've once seen a report that stated that the average swimmer can make it about 50 meters max in 4°C water before drowning. That is not a lot! Meaning, that if the person in distress cannot hold on to something which helps them stay afloat you have very little time at your hands.
Ice is incredibly dangerous. If the person in distress just broke through a layer of ice it will be almost impossible for them to rescue themselves, unless they have the right tools and experience (or the water is very shallow). It should also be obvious that it is very dangerous for yourself to go anywhere near the place where the ice was broken. If you cannot avoid this, try to spread out your weight, i.e. lie on your belly and spread all fours. Use whatever you can to extend your reach, such as a belt/jacket/backpack strap.
