Yes, I would be surprised if it was more popular somewhere else. And sauna itself is a Finnish word.
Ice swimming (avantouinti) on its own is especially popular in Estonia and Finland. There is an Avantouinti Society, and swimming holes are also maintained by other groups such as the Finnish skiing association (Suomen Latu). The Finnish Sauna Society maintains an avanto for sauna goers.
There are lots of places where you can swim without sauna in Finland during winter. Helsinki has several places for avantouinti, with dressing-rooms and sometimes with saunas. There is also a number of ice swimming and winter sauna locations around Tampere.[1]
I was under the impression "winter swimming" translated to "avantouinti", but apparently not. Ice swimming is where it's at.