Hadith: If one of you makes ablution and then wears his leather socks, then let him wipe over them (in his next ablution) and pray while having them on without taking them off, except if he becomes in the state of Janābah

عن عمر -موقوفا- وعن أنس رضي الله عنه مرفوعا: «إذا توضأ أحدكم ولبِس خُفَّيْه فَلْيَمْسَحْ عليهما، وليُصَلِّ فيهما، ولا يخلعْهُما إن شاء إلا من جَنابة».
[صحيح] - [حديث عمر -رضي الله عنه-: رواه الدارقطني. حديث أنس -رضي الله عنه-: رواه الدارقطني]

‘Umar and Anas (may Allah be pleased with both of them) reported that the Prophet (may Allah's peace and blessings be upon him) said: "If one of you makes ablution and then wears his leather socks, then let him wipe over them (in his next ablution) and pray while having them on without taking them off, except if he becomes in the state of Janābah." The report of ‘Umar is Mawqūf (the chain of narrators stops at his level without attribution to the Prophet), while the report of Anas is Marfū‘ (directly attributed to the Prophet).
Sahih/Authentic. - [Ad-Daaraqutni]

Explanation

If someone wears his two leather socks after making ablution, then something nullifies his ablution and he wants to make ablution again, it is permissible for him to wipe over them, then pray in them and not take them off for that would be hard and difficult for him. Rather, he can wipe over them as a way of making things easy and alleviating hardship for this Ummah. However, if he becomes in the state of Janābah, in that case he must take them off and take a ritual bath even if there is time remaining for the period of wiping over them. Based upon this, wiping is only permitted when making ablution.