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All regulators can freeze up if used improperly (e.g. dry breathing at surface) or if conditions get really rough. The better regulators are just less likely to do so.
The most popular regulator used today for cold water conditions both in terms of over all sales, and independent testing is the Sherwood Maximus.
From a U.S. point of view, perhaps. Personally I believe U.S. cold-water divers number less than, say, UK and Scandinavian cold-water divers combined (but I may be wrong). My guess is that the most popular cold-water regulator is the Apeks series (above TX20 level), in competition with the Poseidon series. Yes, I regularly see Poseidons free-flow in winter, but since my own DS4/TX50 free-flowed this fall on the surface after being serviced (and the flow probably set to high) I'm not so cocky ...
Then again, the Aqualung Glacia series is effectively a rebranded Apeks TX50, but considerably cheaper where I live. One of my buddies has dived it, and it's a great reg. Nowadays he dives a Divex (the Swedish make, not the UK one) and that is a superb regulator. I've never seen one play up. Personally, I'm happy with my Apeks, which has never let me down while actually diving. And the US Antarctic Program are happy with their Sherwoods and the U.S. Navy are happy with their Poseidons (as are the Swedish Navy, BTW.
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There are a lot of good regs out there, but you really have to know how to use them in cold-water conditions.