I do not think chocolate milk comes from brown cows, as allegedly 7% of US adults do, see below.
However, I do still instinctively feel that brown eggs are better for you than white ones.
Stands to reason, doesn’t it? Brown rice, brown bread, brown eggs are all good for you. Also probably brown trout, brown sugar, hash browns, hash brownies, Newcastle brown ale and brown noise.
https://www.livescience.com/59666-do-people-believe-chocolate-milk-from-brown-cows.html