بسم الله الرحمن الرحيم
At the time of the Prophet ﷺ,
women were keen to cover themselves completely, and this
included covering the feet. For this reason,
they used to let the hems of their garments hang low, even allowing them to touch the ground.
This itself shows that
covering the feet was understood to be required, otherwise there would have been no need for concern over the hem dragging on the ground.
A woman asked
Umm Salamah رضي الله عنها, the wife of the Prophet ﷺ:
“I am a woman whose garment drags, and I may walk through a dirty place.”
She replied:
«يُطَهِّرُهُ مَا بَعْدَهُ»
The Messenger of Allah ﷺ said:
“That which comes after it purifies it.”
References:
Reference: Sunan al-Tirmidhi: 143
Reference: Sunan Abi Dawud: 383
Reference: Sunan Ibn Majah: 531
Classed as
Sahih by Shaykh al-Albani
Reference: Sahih Abi Dawud: 407

This indicates that
women deliberately allowed their garments to trail in order to
cover the feet, even at the risk of dirt.
Ibn ‘Umar رضي الله عنهما narrated:
The Messenger of Allah ﷺ said:
“Whoever lets his garment drag out of pride, Allah will not look at him on the Day of Resurrection.”
«قَالَتْ أُمُّ سَلَمَةَ: فَكَيْفَ تَصْنَعُ النِّسَاءُ؟ قَالَ: يُرْخِينَ شِبْرًا، قَالَتْ: إِذًا تَنْكَشِفُ أَقْدَامُهُنَّ، قَالَ: فَذِرَاعًا لَا يَزِدْنَ عَلَيْهِ»
Umm Salamah رضي الله عنها 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.”
References:
Reference: Sunan al-Tirmidhi: 1731
Reference: Sunan al-Nasa’i: 5336
Classed as
Sahih by al-Albani
Reference: Al-Silsilah al-Sahihah: 1864

This clearly shows that
the exposure of the feet was not acceptable, and that garments were lengthened
specifically to cover them.
Based on these narrations:
It is not permissible for a woman to wear open footwear that shows her feet.

If her garment is long enough to cover her feet, this fulfills the requirement.

If she wears socks under a long garment, there is
nothing wrong with that, although
covering the feet with the garment itself is better.
Shaykh al-Islam Ibn Taymiyyah رحمه الله
He 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 which shows the shape of the foot, because this is worn by men.”
Reference: Majmu‘ al-Fatawa: 22/148
Shaykh Ibn ‘Uthaymin رحمه الله
He 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.”
Reference: Fatawa al-Mar’ah al-Muslimah: 1/437
And Allah knows best.