Hi Chung
It looks like you're new to the site, so welcome.
Costume history is a fascinating discipline and the subject of dress has already been discussed in great detail on ET. For starters, I'd refer you to the 'Passenger Fashion Gallery' thread, which was started in spring last year, and which can be accessed by clicking on 'Passenger Research' and the subheading 'General - All Classes'.
Many first-class passengers were prominent members of European and American 'Society' and their outfits at the parties and functions they attended were minutely described by journalists and gossip columnists. No doubt you're aware, too, that one of the most successful and influential fashion designers of the Edwardian Era,
Lady Duff Gordon, was aboard the 'Titanic'. The insurance claims for lost luggage filed after the sinking by the likes of Charlotte Cardeza, Leontine Aubart and Emma Bucknell provide us with wonderful insights into what the wealthier passengers carried in their trunks and suitcases.
Hats were very much part of day-to-day wear for all classes in 1912 and so would certainly have been worn by both men and women aboard the ship. I'm not aware if any of the third-class passengers would have worn head-scarves for religious reasons but close inspection of 'Titanic' survivors boarding the '
Carpathia' early on the morning of 15th April reveals many women with blankets and shawls tied around their heads. I don't believe that these are all steerage passengers - as I've speculated elsewhere, I think the terrible cold that night forced many in the lifeboats to bundle themselves up any which way in an effort to keep warm.
Good luck with your research!
Best wishes
Martin