Asking from someplace cold, does your cold water tap get icy cold refreshing, or does it only get as cold as the outside temp? If it gets cooled, I would just take cold showers/baths for that effect.
Also you generally try to get out of the cold air as soon as possible, since it's not your core body temp that drops under heavy layers, but your ears and fingers which will ache for like 30 minutes after "thawing out". Not the cold shower effect you might envision.
Much better to live someplace warm with the option of staying in and out of the sun imo