For further reading:
https://divelab.com/download/proced...ubaRegulatorFreezing-ChillingFacts-4-9-14.pdf
cold water | John Clarke Online
Why Scuba Diving Regulators Freeze
And for more extreme conditions:
Cold Water Regulator Blues
Cold Water Scuba Regulator Testing — U.S. Navy vs. EN 250
https://apps.dtic.mil/dtic/tr/fulltext/u2/a304487.pdf
I think most of these have been linked to on scubaboard before, and the topic comes up from time to time.
Fascinating subject to me as my diving is likely to get slightly deeper and colder in the next few years. (Not much -- just talking about recreational depths in the Great Lakes, possibly, but that can get pretty cold.)
As far as I can tell, there is no real consensus on what is a "safe" temperature for any reg. Below water temperatures of 50 degrees (or even a little higher) the odds of a free flow are increasing with the drop in water temperature, and can depend on outside air temperature before the dive starts, breathing rate, tank pressure (pressure drop), depth, regulator design, and the potential for water vapor inside the regulator. The ultimate answer would be to have redundant first stages (pony tank, doubles, H-valve).
The problem is that most testing (at least publicly available testing) seems to be done under fairly extreme conditions -- very cold water and very high breathing rate. That's good in the sense that it gives you an idea where things will fail. On the other hand, it doesn't give you a clear sense of what might be likely on a normal "cold" dive for those of us that will never dive in Antarctica. For example, an "easy" dive on a warm spring day where the bottom temp of the quarry might be 47 degrees at 50-60 feet.
I saw an ambulance pull up at a local quarry after someone had a free flow and apparently shot to the surface quickly. (Heard the story second hand -- saw the ambulance there.) Makes you think a little bit more about it.