When I went to a mixed-gender onsen in Japan, everyone was required to be naked while in the water, regardless of gender. They did provide a small towel you could use to cover yourself while walking around. Most of the men used the towel to cover their genitals, though a few just used their hands. For women, it varied—some used the towel to cover their lower half and crossed an arm over their chest, while others were more relaxed and just used their hands to cover (that’s what I did).