I don't normally post here, but I felt it worth chiming in to mention that the Shrouded Cowl does not actually infer the benefits of the Matching Set perk. The jump in Armor Rating that you're seeing is from the Custom Fit perk which is a prerequisite for Matching Set. If Matching Set were kicking in, the Armor Rating would be even higher.

If there are any doubts put on a set of vampire armor (normal or royal, it doesn't matter), highlight the cowl without putting it on. Then, calculate the normal armor rating if adding the Cowl, then add 25% to that number. That's the Custom Fit bonus. Finally, calculate an additional 25% for the Matching Set bonus (or even just an additional 50% from the base total) and equip the Cowl. The numbers don't match up for having both bonuses, considering the full set is light armor and therefore benefits from Custom Fit.