The history of warfare is replete with soldiers who excelled in extreme weather.
There was Rommel's Afrika Korps versus the British Desert Rats. They fought back and forth across the Sahara for two years in blazing heat and brutal sand storms.
Finnish ski troopers fought off a Soviet invasion during the winter of 1939-40 in temperatures below -40 degrees. It was only with the spring thaw that the outnumbered Finns had to sue for peace.
$20 billion on air conditioning. Per year. For perspective, that is more than the gross national product of Afghanistan. We could buy the whole freaking country for what it is costing to keep our soldiers comfy.