Is a woman obliged to wear socks when she is outside the home or while praying?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad  is His slave and Messenger.

Women should cover their feet during prayer whether  they pray at home or outside. They should also cover their feet with thick socks when in presence of Non-Mahram men. They may use their dress to cover their feet if this dress is long enough to conceal the feet even while a woman is walking. They may also use any thick piece of cloth to wrap their feet if they can not find socks.

The evidence for this is the Hadeeth reported from Ibn 'Umar  that the Prophet  said: "Whoever drags his lower garment out of pride, Allaah Will not look at him on the Day of Judgement" Umm Salamah said to the Prophet: "What should women do with their lower garments (which are dragged behind them)" The Prophet replied: "They should drag it for a hand span" Umm Salamah  said: "But their feet would get uncovered". The Prophet  said: "Then they should drag it a Thiraa' (about a yard) and no more than that". [An-Nasaa'i and At-Tirmithi]

Allah knows best.