I'm afraid it would not suffice.

From the recent best selling book Head Strong

By strategically and temporarily stressing your body, you can boost its natural detoxification systems and stimulate the creation of new mitochondria to maximize your energy. (p. 39)

Just taking a cold shower for one minute in the morning is often enough to stimulate cold thermogenesis. (p. 175)

The cold water is an acute stressor that does good. General cold weather doesn't exactly do the same thing.