From Longman Dictionary of Contemporary Englishblue with coldblue with coldespecially British EnglishCOLD someone who is blue with cold looks extremely cold → blue
Examples from the Corpus
blue with cold• Doug emerges from the cabin looking blue with cold.• Gerda approached Kay, who was blue with cold but oblivious to his predicament because of the ice in his heart.• Ben, naked except for the strait-jacket, and blue with cold, was heaving and struggling and bellowing. 