How authentic is the attribution to Umar ibn al-Khattab (may Allah be pleased with him) of the will concerning preparation for winter with wool, khuffs (leather socks), and regular socks, and the statement that "cold is an enemy swift in its entry, distant in its departure"?

This admonition was mentioned by Ibn Rajab al-Hanbali in "Lata'if al-Ma'arif," where he narrated from Ibn al-Mubarak, from Safwan ibn Amr, from Sulaym ibn Amir, that Umar ibn al-Khattab, may Allah be pleased with him, used to advise people upon the arrival of winter to prepare for it with wool, khuff (leather socks), and jawarib (socks), and to make wool their شعار (inner garment) and دثار (outer garment); because cold is a swift-entering enemy, slow to depart. No ruling from scholars regarding the authenticity or weakness of this admonition has been found.