Greg - I've been doing the police diver thing for about 5 years now. Our team has between 120-150 callouts a year. Unfortunately, even though intentions may be good, the dangers inherent in doing any kind of rescue would probably preclude doing them without SIGNIFICANT training and practice, especially when it comes to doing them under ice.
Our team has everyone in Viking drysuits, AGA full-face masks, with Buddyphone comm units, and a ton of specialized gear, from ropes to drop tanks, to search grids, and we hate diving under ice, due to the risk factors involved. Does that mean we don't do it? Absolutely not...just that ice dives are at the very bottom of our "OH BOY!! We get to dive!!" list. Add in zero vis, and it really sucks. Not only do you have to worry about everything else generally associated with diving, but you are now diving in an environment that is usually less that hospitable (rebar, trees, chemicals, etc.) Entanglement is always a concern for us. Add the fact that on ice dives, we are all tethered, and there is yet another possible entanglement point to worry about. Air goes more quickly, and gauges are almost impossible to see.
The bottom line is that although there have been SOME (very, very, very few) cold water rescues, and although the mammalian dive reflex is a wonderful theory, chances of a rescue are much closer to the "none" category, than to the "slim" category.
Now then, if it's your kid, these concerns will mean absolutely nothing...however, in an underwater under-ice search you are likely to add your body to the one we will already have to pull out.
If you are interested in good courses on the subject, the National Academy of Police Diving (NAPD), Dive Rescue International, and Lifeguard Systems all offer good courses. I'm not sure if all of them allow non-public safety divers access to the courses, but they are great courses nonetheless. However, these skills must be practiced religiously, or they fade. Also, you will need (at the minimum) 3 divers and a tender that know what they are doing, in order to even begin to do such an op safely.