I have been diving the Midwest for more than thirty years and have dived the deep cold water of the Great Lakes and done many under ice dives in the smaller lakes and quarries. I certainly have had my share of iced-up free-flowing regulators. As a charter captain I have seen many cases of free-flowing regulators in others.
In the initial stage, the regulator just does not quite shut off during the exhalation part of the breathing cycle. The factors that cause icing include cold water, heavy breathing and higher air density (depth). It slowly increases as ice forms in the first stage pushing on the spring and forcing the first stage valve completely open. A fully open valve can empty a full 80 CF tank in 20 to 30 seconds.
I have seen some divers advocating kinking the low pressure hose to shut down a free-flow. Although I have never tried this, if you could king the hose the hose would explode, since their burst pressure is in the range of 450 psi. I did see a hose explode once when a diver had a first stage frozen open and a second stage frozen closed. (This was not during the dive but on the surface after the dive when the diver went back to his equipment and turned the air back on.)
The real key to handling a free flow is to recognize the problem early. A free-flow, in my experience takes about two to four minutes to progress from the point where it is just noticeable to the point at which it causes a fully open valve. If a diver recognizes that a freeflow is starting early it is quite easily managed merely by terminating the dive. I have actually continued to work on a task at a 100 ft+ depth while my regulator had already begun to free-flow, knowing that I still had plenty of time to finish what I was working on and still make a normal ascent. The bottom line is that this kind of equipment problem is perfectly manageable and should not be an emergency for an experienced diver.