To cover or not to cover, that is the Western woman's question. Well, the first 3/4 of my trip I did not cover my head. The last 1/4 of my trip I did. I found that I was a lot more respected, even spoken to in Arabic and blended in much better when I covered my head. It is your own choice obviously, but always bring a scarf with you in your purse when going out. You never know where or when the Muttawa (religious police) is lurking. I never had any problems with the Muttawa - only to have them tell me politely to "please cover my head".
If you are a woman and travelling to Saudi Arabia be prepared to wear a conservative clothing when arriving to the Kingdom(i.e.long pants and jacket or long sleeved shirt).
Buy an Abayah in Saudi Arabia after you arrive.(it`s something like a cloack )
Although it is considered "OK" not to have your hair covered as long as your not a Saudi,but you`ll find yourself more comfortable wearing it.
No one should forse you to cover your face,I never do ;-)
Here is a picture of my own Abayah,year 2004 collection had is the chinese symbols theme(kinda exotic to us)You will find an Abaya that matches your taste and budget
When a woman living in Saudi Arabia appears in public, she normally wears a voluminous black cloak called an abbeya, a scarf covering her hair and a full-face veil. There are varying opinions regarding the wearing of the abbeya and hijab (literally curtain or veil); however, Saudi women cover themselves in public and in the presence of men who are not close relatives.
Women's fashions do not stop with the abbeya, though if you are a male, that is all you are likely to see. Beneath the black cloak, Saudi women enjoy fashionable clothing and take great pride in their appearance. They enjoy bright colours and lavish material.
As mentioned by others as a female you will feel much more comfortable with the abaya on (it is NOT required though) however I have never covered my hair nor do the majority of expats I know or see. I think that the old custom of not being in a room or elevator with a non-relative female is dying out as I have been in many a mall elevator with plenty of people I haven't been related to - LOL! However as a woman do not expect to shake hands with any local man here.
I have lived here four years and have found that it is difficult to get to know, or find the opportunity to meet, Saudis. Once you do however you will find them to be very warm and friendly - except when it comes time to stand in a line at a checkout counter!