I know covering feet is a part of the women’s hijab. But can a woman wear skin tone socks to cover the feet or does that disregard the purpose of socks as it looks like the woman’s skin color?

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If the socks are transparent then it is haraam.
If a woman is wearing non transparent socks which are skin colour but it is coupled with a dress that is attractive and the socks add to it in such a way that it attracts attention of the opposite gender then again it is haraam.
If the socks are non transparent and cannot be mistaken for a woman's foot and do not draw attention of the opposite gender then there is no problem in wearing them