Does the girl who wears Hijab have to cover her feet?

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.