A question regarding wiping over socks

Question:
I put on socks after performing wudu and achieving complete ritual purity. Then, after one or two time periods, I put on another pair of socks to protect against the cold, while I was in a state of ritual impurity. Is it permissible to wipe over the second pair of socks?

Answer:
He mentions that he put on the socks while in a state of purity. After one or two time periods had passed, he put on another pair of socks for warmth, and he had become ritually impure, so he was not in a state of purity.

And the answer: He does not wipe over the second pair of socks; it is not permissible, because he put them on while not in a state of purity. However, if he had put them on while in a state of purity—meaning he performed wudu and wiped over the first pair of socks, then put on the second pair while in a state of purity—then wiping over them is permissible, because he put them on while in a state of purity.
As for if he put them on after becoming ritually impure, then he put them on while not in a state of purity, so he does not wipe over them.