Is it permissible to perform prayers without covering feet?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

According to the view of the majority of the Muslim scholars, a woman has to cover her feet while performing the prayer.

Umm Salamah asked the Prophet if a woman can pray in a long shirt (like a thick night shirt) and head covering without a loincloth. The Prophet said: “If the shirt is long and flowing and covers the top of her feet.” [Abu Dawood, and al-Hakim who said: “It is a sound Hadeeth.”, and ath-Thahabi endorsed this.

So, a woman is not obliged to wear socks as long as her shirt is long as described above, and there is no problem if she wears it [the shirt].

But, if the shirt does not cover her feet, then she has to wear such socks to cover her feet.

Allah knows best.