Just “living in a cold climate” doesn’t have a particularly adverse effect on health, I think. But being unprepared for extreme cold certainly can.
Several years ago I read a true account of the Children’s Blizzard of 1888 in the American Midwest. It was a particularly fast-moving and wickedly cold storm that caught everyone by surprise, especially by surprise since it came in so quickly and forcefully after a long period of shirt-sleeve warm winter weather that everyone was enjoying.
What happened, in fact, was that the blizzard struck without advance warning during a weekday when most children were at school. Some schools let children out early, and they began walking home. Many were lost and killed that way, and many more who hadn’t lost their way were still killed by exposure and unpreparedness.
Some students (and teachers) who sought shelter in the outdoors or in the school buildings themselves did manage to survive the day and night of the storm, but in documented case after case, when they emerged from their relative shelter into the calm, but brutal cold of the next morning, even when rescuers were in plain sight, they dropped and died very quickly due to that extreme cold.