Hadith: If any of you makes ablution and puts on his leather socks, let him pray while having them on, and let him wipe over them without taking them off, if he wishes, except in the state of Janābah (major ritual impurity)

عَنْ أَنَسٍ رضي الله عنه أَنَّ رَسُولَ اللَّهِ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ قَالَ:
«إِذَا تَوَضَّأَ أَحَدُكُمْ وَلَبِسَ خُفَّيْهِ فَلْيُصَلِّ فِيهِمَا، وَلْيَمْسَحْ عَلَيْهِمَا ثُمَّ لَا يَخْلَعْهُمَا إِنْ شَاءَ إِلَّا مِنْ جَنَابَةٍ».
[صحيح] - [رواه الدارقطني] - [سنن الدارقطني: 781]

Anas (may Allah be pleased with him) reported that the Messenger of Allah (may Allah's peace and blessings be upon him) said:
"If any of you makes ablution and puts on his leather socks, let him pray while having them on, and let him wipe over them without taking them off, if he wishes, except in the state of Janābah (major ritual impurity)."
[Authentic hadith] - [Narrated by Ad-Daraqutny] - [Sunan Ad-Daraqutny - 781]

Explanation

The Prophet (may Allah's peace and blessings be upon him) clarifies that if a Muslim puts on his leather socks after performing ablution, then later he becomes in the state of Hadath (minor ritual impurity) and wants to make ablution, he is permitted to wipe over them if he wishes. He can pray while having them on without taking them off for a specific period unless he becomes in the state of Janābah, in which case he must take off the leather socks to take a ritual bath.