To wear a woolen cloak during the Ghazawat

Narrated Al-Mughira:

One night I was with the Prophet on a journey. He asked (me), "Have you got water with you?" I replied, "Yes" So he got down from his she-camel and went away till he disappeared in the darkness of the night. Then he came back and I poured water for him from the pot (for the ablution). He washed his face and hands while he was wearing a woollen cloak (the sleeves of which were narrow), so he could not take his arms out of it. So he took them out from underneath the cloak. Then he washed his forearms and passed his wet hands over his head. Then I tried to take off his Khuffs, but he said, "Leave them, for I have performed ablution before putting them on." And so he passed his wet hands over them

حَدَّثَنَا أَبُو نُعَيْمٍ، حَدَّثَنَا زَكَرِيَّاءُ، عَنْ عَامِرٍ، عَنْ عُرْوَةَ بْنِ الْمُغِيرَةِ، عَنْ أَبِيهِ ـ رضى الله عنه ـ قَالَ كُنْتُ مَعَ النَّبِيِّ ﷺ ذَاتَ لَيْلَةٍ فِي سَفَرٍ فَقَالَ " أَمَعَكَ مَاءٌ ". قُلْتُ نَعَمْ. فَنَزَلَ عَنْ رَاحِلَتِهِ، فَمَشَى حَتَّى تَوَارَى عَنِّي فِي سَوَادِ اللَّيْلِ، ثُمَّ جَاءَ فَأَفْرَغْتُ عَلَيْهِ الإِدَاوَةَ، فَغَسَلَ وَجْهَهُ وَيَدَيْهِ، وَعَلَيْهِ جُبَّةٌ مِنْ صُوفٍ، فَلَمْ يَسْتَطِعْ أَنْ يُخْرِجَ ذِرَاعَيْهِ مِنْهَا حَتَّى أَخْرَجَهُمَا مِنْ أَسْفَلِ الْجُبَّةِ، فَغَسَلَ ذِرَاعَيْهِ، ثُمَّ مَسَحَ بِرَأْسِهِ، ثُمَّ أَهْوَيْتُ لأَنْزِعَ خُفَّيْهِ فَقَالَ " دَعْهُمَا، فَإِنِّي أَدْخَلْتُهُمَا طَاهِرَتَيْنِ، فَمَسَحَ عَلَيْهِمَا ".