Q. My mother was very careful not to let her children walk around the house while wearing only socks. Is there a source for such a minhag?
A. Nitei Gavriel (Bein Hametzorim 2: 94: 1: n. 4) indeed mentions that since people in mourning walk around when only wearing socks, people abstain from doing so. (Since it may be opening the mouth for one being charged by the forces of evil). He mentions the above in regard to avoiding taking off shoes when it still is Shabbos before Tisha Beav begins, as one is showing open avelus on Shabbos.
Regarding wearing only socks, Horav Shlomo Miller’s Shlit’a opinion is that people should maintain the minhogim and traditions of their families.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller Shlit’a and Aharon Miller Shlit’a