I... have a beard and I was explicit about not shaving anything. Thanks for the "reminder," but:
If you're shaving off your body hair, then you're
defeating Mother Nature's most effective air conditioning,
and you're going to ensure that your sweat slides uselessly
down your legs before it can help your body cool down.
Hey sorry, this does not happen.
I've spent many, many hours in the sun (sports, yard work, hiking) including in muggy 95F/35C+ summers over the years. There are days where I have consumed gallons of water just to replace what I've sweated out.
Wouldn't exactly be hard to detect. If it was literally running down my legs with no chance to evaporate then it would be pooling in my socks and shoes or leaving trails of sweat on the tennis court. Never seen this happen to me or anybody else in person or on TV. And certainly you don't see this on televised sports. You don't see leg hair-less people passing out or dripping sweat onto the playing surfaces in basketball, tennis, etc.
One tends not to see much body hair on native equatorial people, either.
Body hair may serve other sorts of cooling purposes. Certainly the hair on our heads (if we're lucky enough to have it) protects us from the sun. And thick enough body hair may do that as well. Really not buying the sweat thing though.