Essentially there are four ways we lose heat. Evaporation is one of them.
Preventing evaporation is important in cold weather to prevent hypothermia.
Producing evaporation is important in hot weather to prevent overheating.
Virtually all air-conditioning systems use evaporation as the mechanism to cool the air. From the old swamp coolers, to kids running in the sprinklers, to heat pumps, it's all about controlling evaporation.
For cold weather survival (I lived in Alaska 26 years) it is essential not to sweat. Sweat makes insulation damp, and when it evaporates much heat is lost. The application to backpacking is to constantly take off layers when going uphill (exertion) to stay cool and prevent sweating, then adding layers at the top to prevent getting cold. I've been snowshoeing steep slopes in zero degrees in shorts and t-shirt and fully comfortable, but more importantly, when I get to the top I put dry layers back on which keep me warm.
For extreme arctic cold, to prevent any dampness to get into insulation, adventurers use vapor barrier layers (VBL - waterproof layer between skin and clothing) to keep insulation dry. It can be uncomfortable at first during times of exertion when the body gets hot and starts to sweat, but if you live with the dampness for a little bit, sweating stops as soon as the air around the skin hits 100% humidity.
For hot weather, we induce evaporation to stay cool. Water it turns out is much more effective coolant than sweat.