Covering the face is not integral to the modest attire (also known as hijab) prescribed for women in Islam; if it had been obligatory, then the Prophet (peace be upon him) would have said so plainly and clearly.

We find nothing in the sources indicating that; rather he told Asma who appeared  before him in an attire less than modest: O Asma when a woman attains puberty she is not supposed to expose any part of her body in front of strangers except her face and hands.”

We also know that women are not allowed to cover their faces in Salah or while in a state of Ihram in Hajj or `Umrah. Based on these, Imam Ibn Jareer and others have rightly said: Covering the face is not a prescribed requirement for women in Islam.

Now coming to the issue of women posting their pictures on the Facebook and others, it is still important for women to exercise caution.