Ruling on wearing one pair of socks over another when one did wudoo’ wiping over the first pair

Yes, it is
permissible to wipe over the second pair of socks if he put them on over
socks that he had wiped over, because he put them on when he was in a state
of purity. So that comes under the general meaning of the words of the
Prophet (blessings and peace of Allah be upon him) in the hadeeth narrated
by ‘Urwah ibn al-Mugheerah from his father who said: I was travelling with
the Prophet (blessings and peace of Allah be upon him) and I reached out to
take his khufoof (off his feet) and he said: “Let them be, for I put my feet
in them when they (my feet) were pure (after doing wudoo’).” And he wiped
over them”

Narrated by
al-Bukhaari, 199 

An-Nawawi
(may Allah have mercy on him) said: If he put on the khufoof (leather
slippers) when he was in a state of purity, then he broke his wudoo’ and
wiped over them, then he put on the jarmooq (a kind of large khuff that is
worn over the regular khuff) when he was in a state of purity in which he
had wiped over the khuff when he did wudoo’, then there are two well-known
opinions as to whether it is permissible to wipe over them (the jarmooq).
The first opinion is that it is permissible to wipe over them because he put
them on when he was in a state of purity. And the second opinion is that it
is not permissible, because that was an incomplete purification. That is how
many of the scholars look at it. 

Ar-Rawiyaati
said: The more correct view is that it is not permissible to wipe over them.
Others said that the more correct opinion is that it is permissible to wipe
over them. This is the opinion of Shaykh Abu Haamid. It may be understood
from the words of ar-Raafi‘i and others that this (the second view) is more
correct and it is the view that is to be favoured, because he put them on in
a state of purity. Their saying that it is an incomplete purification is not
acceptable. 

End quote
from Sharh al-Muhadhdhab, 1/534 

Shaykh Ibn
‘Uthaymeen (may Allah have mercy on him) said: If he put on khufoof then
broke his wudoo’, then he wiped over them, then put another pair of khufoof
over the first pair when at the time of putting on the second pair, he is in
a state of purity for which he wiped over the first khufoof, then the view
[i.e., the view of Imam Ahmad] is that the ruling on wiping applies to the
first pair, because he put on the second pair after breaking his wudoo’. 

Some of the
scholars said: If he put on the second pair when he was in a state of
purity, it is permissible for him to wipe over them, because it is true to
say of him that he put his feet into them when they were in a state of
purity. The Prophet (blessings and peace of Allah be upon him) said: “for I
put my feet in them when they (my feet) were pure.” This includes purity
attained by both washing and wiping. This is a strong view, as you can see,
and it is supported by the fact that our companions (may Allah have mercy on
them) stated that wiping over the khufoof removes impurity. So he put on the
second pair when in a state of complete purity, so why shouldn’t he wipe
over them? But if he put the second pair on when he did not have wudoo’,
then he cannot wipe over them because when he put them on he was not in a
state of purity. 

End quote
from ash-Sharh al-Mumti‘, 1/258 

And Allah knows best.