Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is best for Muslim women to wear socks while wearing flat shoes. This is based on the majority view that a woman must cover her feet while venturing out.
Responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
It is best for Muslim women to wear socks while wearing flat shoes. This is based on the majority view that a woman must cover her feet while venturing out. However, Imam Abu Hanifah and Ibn Jarir do not think it absolutely necessary to do so.
The authentic and preferred view in the Shafi`i school is that women’s feet are awrah. This view is also shared by Imams Malik, Al-Awza`i, and Abu Thawr- as stated by Imam An-Nawawi in his encyclopedic work al-Majmu`. Imam Abu Hanifah, Sufyan al-Thawri, and Muzani, however, do not consider women’s feet as awrah.
There is no harm in following the latter view in case of hardship. It is acceptable to do so, according to the teachings and precedents of the imams of the madhhab.
Source: AsktheScholar.Com
Almighty Allah knows best.