Do you think Alucard wears the hat or glasses just to look cool?

petite-strigoi:

For the hat, probably…. I mean what really is the function of a hat other than accessorising ? Or as Mr Hightop would say “The purpose of a hat is to follow the proper dictum of society” (Alice Through The Looking Glass) 

But if you look at his glasses however you will notice that he has the little guards on the side. Now glasses like that would reduce wind and debris blowing into your eyes sideways, so they are most likely to offer protection while he works with his firearms.
Also there is to consider that Alucard day walks and the lenses makes the day light and artificial lights less troublesome to his eyes that are now attuned to darkness.
Though Im pretty sure in the real world lenses for that purpose would be blue.