I try to address the situation you are asking about, even though I think you already did a good job so this may not be overly helpful/new. Additionally in one of your referenced answers that is actually about rescuing someone out of the water, there is already a great answer by D.Lambert on what to do after rescuing, so my answer will overlap greatly (I still do not think the question is a duplicate, more like this answers belonged here). As you are asking for references, I take this information from my favorite outdoor medical guide by the Swiss association for mountain medicine and the Swiss Alpine Club. So the situation as I understand it is, that we have a wet patient which was immersed shortly in icy water. I assume we now are out of danger of falling into water again.
This person will most likely not yet suffering from hypothermia or if so from first stage hypothermia, meaning he will shiver and be apart from psychological shock be of clear consciousness.
If you are very exposed to wind/rain/snow and have the possibility of getting to a somewhat shelter spot in the immediate vicinity - get there immediately. Is such a place further away try to provide some protection by other people, backpacks, ... while stripping the patient and getting him into dry clothes. Ideally these are spare clothes (in cold weather you should have at least some anyway) and what other can spare.
No there are two scenarios: The patient might feel up to moving by himself. In this stage this is optimal, as a lot of heat can be produced by activity. Just start easy and immediately abort if the patient feels dizzy. Otherwise you try to isolate the patient as good as possible. If you have some kind of heating device (like those little chemical bags) put them onto the first layer on the torso, never directly onto the skin. If you have a sleeping bag, get the person in it, then use rescue blankets, bivy bags, etc. as an outer protection. Of course if two people fit into the sleeping bag, all the better, that's just another heating device inside. However as mentioned in the comments, this may be of limited help. It is likely the person can do more good on the outside (transport, shelter, fire, ...) than he helps inside the bag (thanks Roddy). Unless psychological issues are included, then the cuddling can be highly effective :)
A person in this stage should be given hot liquids to drink, preferably sugary, and motivated to move, even in the sleeping bag. After these initial steps you want to get to a sheltered area. Without such a place you need to improvise: Create some shelter against wind (e.g. snow cave, beside a rock, under tree using branches) and start a fire. This is a whole topic on its own. Thus further cooling should be preventable and if there are not further injuries the patient should recover and immediate evacuation to a hospital is not necessary.
However if you cannot accurately protect the patient it can get life threatening fast. Its out of scope, but just as a warning: When the patient consciousness gets clouded and/or stops shivering this may already be stage two hypothermia. You cannot do much more than prevent further heat loss, but now the patient should not be actively moved and not given anything to drink, unless he is on clear conscious (danger of aspiration). In this case organize evacuation asap and be on alert to perform CPR and remember: A patient with hypothermia is never dead unless he is warm and dead.
Addressing your specific questions:
- Useful gear:
Sleeping bag, bivy bag, chemical heating thingy, rescue blanket and thermos flask (with hot liquid) (I know, kinda obvious and not very light-weight).
- Correctness of stated example:
Well as far as it was described, sounds good to me.
- Most immediate/primary concern:
Prevent further heat loss (again, obvious) - the rest follows.
- Day hike with limited gear:
Improvise the heck out of the situation. In this situation the chance is big, that you cannot provide ample protection from the cold, but on a day hike external help should be fairly quickly available - do not lose time, organize help immediately if in doubt about whether you can handle it on your own.
Reference:A.G. Brunello, M. Walliser, U. Hefti, Gebirgs- und Outdoormedizin (SAC Verlag, Bern, 2011), p.232.