All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
It is prohibited for the woman to wear whatever is peculiar to men of clothes or shoes and the like. There are many texts which state the prohibition in this regard, and these texts are general in nature and do not restrict this to a short or long time. Regarding shoes in particular, Ibn Abi Mulaykah reported that when someone told ‘Aa'ishah, may Allah be pleased with her, that a certain woman was wearing (men's) sandals, she said, "The Messenger of Allah, sallallahu ‘alayhi wa sallam, cursed the mannish woman." [Abu Daawood - Al-Albaani graded it saheeh (sound)]
Mulla Al-Qaari wrote in his commentary on the hadeeth, "The hadeeth refers to the woman who wears shoes that are peculiar to men ... He cursed the woman who imitates men in their clothing or way of talking ..." [Mirqaat Al-Mafaateeh]
Shaykh Ibn ‘Uthaymeen said, "It is prohibited for the woman to wear clothes that are peculiar to men, be it in the prayer or otherwise, because it was authentically reported that the Prophet, sallallahu ‘alayhi wa sallam, cursed the women who imitate men and the men who imitate women. It is impermissible for the woman to wear a garment that is peculiar to men."
This applies to the clothes that are peculiar to men. However, whatever is commonly worn by both men and women in any given society, there is no harm that either of them wears it.
We believe that if a woman could not find women's clothes to keep her warm in the cold weather and there was a necessity or real need to wear men's clothes in this situation, then the necessity is to be addressed according to its true proportion.
Allah knows best.