In my experience, no. Swimwear is pretty common, or going in wrapped in a towel, nudity I've only seen in single sex saunas, like the one in the ladies locker room in the gym.

My early sauna experience was at a friend's home. Her family were from Sweden and had put a pool and sauna house in the backyard. The pool was never heated, when we (group of teenaged girls) were over, we'd dive, swim laps until we warmed up, then sauna, repeat swim & sauna. In that city and that culture, nudity would have been unthinkable, as would have been wearing street clothes into the sauna.