Q. I once saw in a shul where the furnace broke on the middle of services an elderly lady putting on two taalis to keep warm, do you have to tell her not to do it?

A. On question 1265 in regards to a woman wearing tefilin we wrote; Horav Shlomo Miller Shlit’”a pointed out to the words of Piskei Teshuvos that although in principle some Poskim would allow women to wear tefillin, since today there are not donned constantly. However, he then vehemently and emphatically quoting contemporary Poskim, rules that nowadays it is totally prohibited, even for a woman perusha (separated from the worldly) and extremely righteous. The reason he explains is that it has become a major issue of Reform Judaism. Besides, he points out to the Targum Yonassan Ben Uziel on the prohibition (Devorim 22: 5) “A man’s attire shall not be on a woman.” The Targum translates the above as applying to tefillin and tzitzis.
Therefore the Rov’s opinion is that a woman should not wear a man’s taalis. (Although since it was used only for protecting her from the cold, some opinions may permit). However, one should procure for her a proper coat or cover to help her keep warm.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a