Allah’s Apostle used to offer the Fajr prayer and some believing women covered with their veiling sheets used to attend the Fajr prayer with him and then they would return to their homes unrecognized.
A woman may veil her face in any way she wants to. The purpose remains the same, nonetheless: to not be recognized by non-mahram men. Feel like a ‘stranger’ in public. Do you? :)
This is one of those incidents that led to the revelation of the verses of Hijab. ‘Umar played an important role in it..
The wives of the Prophet used to go to Al-Manasi, a vast open place (near Baqia at Medina) to answer the call of nature at night. ‘Umar used to say to the Prophet “Let your wives be veiled,” but Allah’s Apostle did not do so. One night Sauda bint Zam’a the wife of the Prophet went out at ‘Isha’ time and she was a tall lady. ‘Umar addressed her and said, “I have recognized you, O Sauda.” He said so, as he desired eagerly that the verses of Al-Hijab (the observing of veils by the Muslim women) may be revealed. So Allah revealed the verses of “Al-Hijab” (A complete body cover excluding the eyes).
Purpose of this hijab: to be unrecognizable. That’s why ‘Umar (RA) stressed so much over it. But sadly, we fail to understand and appreciate its purpose today. May the essence of ‘hijab’ come back to us!