Al-Mughirah bin Shu'bah (May Allah be pleased with him) reported:
I was with Messenger of Allah ﷺ in a journey one night, and he asked me, "Do you have any water with you?" I said, "Yes." So he dismounted from his riding camel and walked away (to answer the call of nature) until he disappeared in the darkness. When he returned, I poured out some water from a vessel and he washed his face. He was wearing a long woollen cloak and could not take out his forearms from his sleeves, so he brought them out from below the cloak and then washed them, and then passed his (wet) hands over his head. I stretched out my hand to take off his Khuff (leather socks), but he said, "Leave them. I put them on after performing Wudu'," and he passed his (wet) hands over them.

[Al-Bukhari and Muslim].

Another narration is: Messenger of Allah ﷺ was wearing a Syrian cloak with tight sleeves.

Another narration is: This incident took place during the battle of Tabuk.

وعن المغيرة بن شعبة رضى الله عنه قال: كنت مع رسول الله ﷺ ذات ليلة في مسير، فقال لي: "أمعك ماء" ؟ قلت: نعم، فنزل عن راحلته فمشى حتى توارى في سواد الليل ثم جاء فأفرغت علي من الإداواة، فغسل وجهه وعليه جبة من صوف،فلم يستطع أن يخرج ذراعيه منها حتى أخرجهما من أسفل الجبة، فغسل ذراعيه ومسح برأسه، ثم أهويت لأنزع خفيه فقال:"دعهما فإني أدخلتهما طاهرتين" ومسح عليهما. . وفى رواية:وعليه جبة شامية ضيقة الكمين. وفى رواية: أن هذه القضية كانت في غزوة تبوك. وفى رواية:وعليه جبة شامية ضيقة الكمين. وفى رواية: أن هذه القضية كانت في غزوة تبوك.