Praise be to Allah.
At the time of the Prophet (blessings and peace of Allah be upon him) women were keen to cover themselves completely, which includes covering the feet. They used to let the hem of their garments hang low. One of them asked the Messenger of Allah (blessings and peace of Allah be upon him) about letting this hem touch what is on the ground, which may make it dirty, and he said: “That which comes after it purifies it.” On another occasion, when he (blessings and peace of Allah be upon him) said that women should let their hems down by one hand span, one of them said, “But then her feet will show.” This indicates that they were keen to cover their feet and that the feet are part of that which must be covered.
A woman asked Umm Salamah, the wife of the Prophet (blessings and peace of Allah be upon him): I am a woman whose garment drags, and I may walk through a dirty place. Umm Salamah said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “That which comes after it purifies it.” Narrated by al-Tirmidhi (143), Abu Dawood (383) and Ibn Maajah (531). The hadeeth was classed as saheeh by Shaykh al-Albaani in Saheeh Abi Dawood, 407.
It was narrated that Ibn ‘Umar (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever lets his garment drag out of pride, Allah will not look at him on the Day of Resurrection.” Umm Salamah said: What should women do with their hems? He said: “They should let them down a hand span.” She said: Then their feet will show. He said: “Then let it down a cubit, but no more than that.” Narrated by al-Tirmidhi (1731); he said: This is a saheeh hasan hadeeth. Also narrated by al-Nasaa’i (5336). The hadeeth was classed as saheeh by al-Albaani in al-Silsilah al-Saheehah, 1864.
So it is not permissible for the woman to wear open shoes which show her feet. But if her clothes are long and she wears socks, there is nothing wrong with that, although it is better for her to cover the feet with the garment and not with socks.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
If a woman wears pants or loose khuff (leather slippers), and the jilbab hangs over it so that the shape of the foot cannot be seen, this achieves the purpose, unlike the tight khuff (leather slippers) which shows the shape of the foot, because this is worn by men.
Majmoo‘ al-Fataawa, 22/148
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
It is permissible for a woman to let her garment down below the ankles. In fact this is what is prescribed for women, so that they may cover their feet. Covering the feet is something that is prescribed for women and is in fact obligatory for them according to many scholars. What a woman should do is cover her feet, either with her garment which is long and covers them or by wearing socks or shoes and the like.
Fataawa al-Mar’ah al-Muslimah, 1/437
And Allah knows best.