Not an halachic question, but we can read many things about talis katan: wool over cotton, tzitzis out or in, etc. It seems that the Lithuanian minhag was to tuck them in, but what about the material? Was it cotton as a majority? What about Slobodka, Mir, Vilna, etc.: any differences?
The modern-day Halachic preference in certain circles for cotton as a material for tallis katan stems primarily from rulings of the Chazon Ish, one of which is that on hot summer days, when it is uncomfortable to wear wool, one does not fulfill the mitzvah of tzitzis with wool. There is a detailed discussion about it here.
The above-mentioned reason is not so relevant to Northern Europe. We may safely assume that the European yeshivos followed the established Halachic practice of the pre-Chazon Ish era, which shows a preference for wool. (Shulchan Aruch Orach Chayim 9:1, Mishnah Berurah ad loc)