So now I’m confused… neither of your answers state that she did in fact cover her hair. Does that mean she didn’t? Or that you don’t know? And what do you mean that hardly anyone saw her? Wasn’t their house open with constant streams of people as is the case with Gedolim, great rabbeim and people who live for the kehilla? Didn’t they have hundreds of shabbos guests? Didn’t the females who where desperate for Brachos and chizuk find a place at her door?
I ask because this is all I know about any and every great tzaddik in litvish and Chassidik circles, past and present, so I always assumed it was the same by the Lubavitche rebbe and Rebbetzin.