Nope. Pure myth. I've met some crazy and "hot headed" chestnuts and also some calm ones, including a mare who let a beginner ride her the second time she was ever ridden. The best trail horse I've ever ridden was also chestnut, and her only temperament flaw was the exact opposite - she was just a bit lazy.
The only possibly supported link between temperament and color in horses is a possibility that pinto horses may be calmer than solid horses due to the link with domestication syndrome.
So, if you're going for a ride and they offer you a chestnut - don't worry. They're not crazy.
In her Paladin's Legacy series Elizabeth Moon assigns a similar superstition about gray or white horses to one of the cultures in her books. So, when worldbuilding, do think whether people in your world have ideas about specific horse colors. But be aware that if your horses are at all realistic, those ideas should be demonstrated to be very, very false.
I mentioned the mare who let a beginner ride her when she wasn't even trained? Here she is.