Is it obligatory for a woman to wear socks, whether praying in her home or elsewhere, knowing that she is not permitted to show anything but her face and hands?

A woman must cover her feet during prayer, both inside and outside her home, and outside of prayer in the presence of non-mahram (definition) men and non-Muslim women. She may cover them with thick socks, or with the hem of her long garment, or with fabric wraps. If she finds nothing but socks, she must wear them. The evidence for this is the hadith (definition) of Umm Salamah (may Allah be pleased with her) when she asked about women's garments, and the Prophet (peace and blessings be upon him) said: "They should lower it a handspan." She said, "Then their feet will be uncovered." He said, "Then they should lower it an arm's length and not exceed that."