I think John Byrne is clearly trying to evoke a black-sporting Batman in almost everything he's done.
Arguably in almost every comic that Batman wears a primarily blue cape and cowl the face of the cowl is always black. So are we to believe that the cowl is literally blue except for this round area directly on the face of the cowl, which is black with blue eyebrows? Or is it conveniently shadowed all the time, even in broad daylight? Or is it supposed to be evocative of black?
You're to believe that the cowl is shadowed.
He's clearly wearing blue, as evidenced by the unshadowed gloves. Most comic book artists have drawn Batman that way when he's depicted as wearing blue, dating back to the early 40's, with that kind of shiny/shadowy look. The visual is obviously an homage to his first appearance, and his "classic" appearance from the Golden Age. He's even drawn with that "shadowed" cowl often in the most modern comics, where he's clearly meant to be wearing black and gray.