All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In Islam, there are symbolic acts that represent the Divine Wisdom. Although it is good to try to search for this hidden wisdom as much as we can, we must carry them out regardless whether their immediate reasons or benefits are clear to us or not.
Uncovering the face for women in the state of ihram while performing Hajj or Umrah is related to the category of ibadat (acts of worship), which are orders of Allah the Almighty.
We believe such acts have infinite wisdom, for Almighty Allah is The All-Wise. He does not order anything unwise, and yet in order for us not to disrespect Allah the Almighty, scholars have classified them as ta`abbudi acts, which means that they are rituals that we must fulfill regardless whether their immediate benefits are clear or not.
Having said this, however, some of the purposes of uncovering the face during the state of ihram for women can be identified as follows:
First, training the soul to surrender to Allah’s commands without questioning His orders, and this constitutes full submission to Allah’s Will. Almighty Allah says: “And it becomes not a believing man or a believing woman, when Allah and His Messenger have decided an affair (for them), that they should (after that) claim any say in their affair; and whoso is rebellious to Allah and His Messenger, he verily goeth astray in error manifest.” (Al-Ahzab 33:36)
Second, the rituals of Hajj and Umrah are very akin to the scenes of the Day of Resurrection when people will be resurrected naked as they were born. The situation will be too hard for them to pay attention to that.
The state of ihram is a symbolic reminder of this Day when everyone will pay no attention save to his own destiny and fate. Similarly, every pilgrim should concentrate only on the rituals of Hajj or Umrah and empty his mind from every concern save devotion to Allah and surrender to His Will.
Third, during the state of ihram, Allah has commanded men not to cover their heads so that they show utter humbleness and surrender to Allah. Equally, a woman is commanded by Allah to do a similar thing that befits her special status (and particular code of dress) by uncovering her face, not her head.
Allah Almighty knows best.