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A group from the dive shop I used recently did an ice diving course in a cold place with ice and snow. It involved cutting through 2 feet of ice to reach real cold freshwater.
The only divers that did not have free flow incidents used Scubapro Mk25 1st stages and G250 or S600 2nd stages. All regulators were specifically tuned to be used for the environment.
And yes, your cold water rated Mk25 1st stage plus appropriate 2nd stage will work well beyond your needs in warm water as well.