No we would be pale like a freshly shaved chimp. As we gradually lost our hair we evolved to have darker skin. When we migrated out of Africa we adapted again to mountains and caves then became pale again.
The key points are both dark and pale skin are evolutionary traits once we lost hair. If you sweat you probably want light skin under fur.
And then you have polar bears, whose main problem is staying warm rather than staying cool or avoiding sunburn. They have black skin and translucent fur so that all of the sunlight is absorbed below the outer insulation layer instead of on top of it.
Also the parts of hair cells that would normally hold pigment are hollow rather than filled with pigment because an air void conducts heat less and thus is more insulating.
Not sure if you are joking, but that's by far the most probable option. Just look at civilizations living for millenia near equator, be it Africa, isolated islands in Indian ocean (ie Nicobar) or native Australians.
Planet was colder, and around equator you actually have quite habitable places even now, deserts are further from equator. But you get tons of light whole year in very stable pattern.
