text: The best way to figure this one out is to look at how much energy it takes to vaporize sweat into the gas phase (per gram of sweat, pretend it's pure water) and how much energy it would take to heat cold water to body temperature.  On a per gram basis, sweating would probably win.  On the other hand, you can drink more cold water than you can probably sweat.  It would certainly feel better drinking the water.