I tend to wear black, brown, navy, or dark gray shorts or tops at WDW (even in August), but as others said, it's all about the fabric. My WDW outfits are made of fabrics that are moisture-wicking, breathable, and light as a feather, and I select styles that aren't tight-fitting or revealing (not for modesty as much as for comfort: any skin that I'm baring isn't getting the benefits of that cooling, moisture-wicking material, and has to get slathered in a layer of sticky sunscreen).*
I understand that scientifically, dark colors absorb more light/heat from the sun, and I did used to adhere to that idea in selecting vacation clothing, but as I've tried various outfits over the years, the only difference I've personally noticed between a white top and a dark one, for me, is that the white one makes me look way fatter in pictures!
*Footnote: Off-topic, but in case anybody cares what I've found works best for my Mom bod (and my bargain-shopper mentality) in 90+ degrees: my favorite go-to shorts are black Duluth Trading Company "Dry on the Fly" shorts intended for boating and fishing, which are super-light and quick-drying, but are still tailored and have usable pockets. For shirts, I have a variety of breezy tech fabric short-sleeved tops (I try to look for ones that have interesting necklines or other details that set them apart from a typical tee) from Walmart, Old Navy, and L.L. Bean. If I want to wear something dressier, I have an L.L. Bean "Fitness Dress" made of tech fabric that is very cool and comfortable, as well as a black Athleta skort dress, designed for hikers. Some of those brands are admittedly expensive, which is why the pricier items were all purchased on eBay or off of clearance racks, at a fraction of the retail price.