Praise be to Allah.
The basic principle regarding socks and regarding water is that they are pure (taahir), and they cannot be deemed impure on the basis of mere speculation. So long as you are not certain that impurity got onto your socks, you do not have to inspect them and think about removing the impurity.
If water reaches the skin of your feet when purifying the socks, that does not matter, and you can still wipe over your socks, so long as you put them on after purifying yourself completely.
The fuqaha’ differed as to whether it is stipulated that the khuff (leather slippers) should prevent water reaching the foot in the first place (i.e., waterproof). Some of them are of the view that this is not stipulated, and this is the view of the Hanbalis. It says in Mataalib Ooli an-Nuha (1/131): The seventh condition is that it should be possible to walk wearing the item that is wiped over, and it does not matter whether it is waterproof or not, because it is covering the part that is obligatory to wash and one can walk wearing it.
Others are of the view that that is stipulated, as is the view of the Shaafa‘is. An-Nawawi (may Allah have mercy on him) said in al-Majmoo‘ (1/531): Is it stipulated that the khuff should be thick and prevent water reaching the foot (i.e., waterproof). There are two views concerning that, both of which were narrated by Imam al-Haramayn and others.
The first view is that that is stipulated, and if the [khuff or sock] is made of woven material such that if water is poured over it, it will reach the foot, it is not permissible to wipe over it.
The second view is that that is not stipulated; rather it is permissible to wipe over it even if the water does reach the foot. This view was favoured by Imam al-Haramayn and al-Ghazaali because it still covers the foot. Our view is the first view. And Allah knows best.
The correct view is that it is not stipulated that the socks should be waterproof, because there is no sound evidence to suggest that it is stipulated that the sock should be waterproof; so long as it is called a sock and people usually wear it, it is valid to wipe over it.
And Allah knows best.