You know how they say “bad things happen in threes” but it’s not really that bad things happen only in threes, it’s that people stop counting after 3? I think it’s the same for stereotypes - we look for small pieces to arrange in a way that is meaningful to us, to justify our preconceived notion that XXYZ should be ZXY way… so we can yell “aha!”.
I really, really don’t give any credence to the stereotype and I think it is just that people see what they want to see. My best boarders have been chestnut. My favorite horse to ride is chestnut. I own exclusively bays (all plain wrappers at that) and still, the chestnut herd-mates are the horses that you can pull out of a field after 3 months of no work and hack around bareback in a halter on… Some of the chestnuts I’ve known you couldn’t pay me to own, but that’s the same for any color: black, grey, pinto, bay…
Of course, a bad apple is a bad apple but I wouldn’t blame it on the fur color… once you start doing that it is a slippery slope… what’s the difference between fur color and skin color?
The only thing I truly believe, and it is backed by science, is that some darker pigmented domesticated species are generally calmer/more tame (rats, pigs, dogs & cats) - but not in horses. That has to do with melatonin.