While skiing in Hintertux, I stayed at the Gasthof Pension Madseiterhof. A remarkably good quality/price ratio! I paid only 80€ per night, which included breakfast and dinner. The rooms are not the newest, but they have a VERY nice sauna at the basement.
There's a nicely lit Finnish sauna, an infrared sauna box, and a relaxation area. And the infrared sauna door handle is made from an old ski! They do not have a pool though, if you're looking for the ultra-luxurious experience, try the Adler Inn (across the street, same management), the Spa Neu-Hintertux (next to the slopes), or the Berghotel Hintertux Wellnesshotel (between the lifts and the Madseiter, but perhaps the best saunas that I have experienced in the world).
Much recommended. The prices of course depend on season, number of people in your party, etc. I was very happy with what I got!
For more sauna and swimming stories, check out planetswimmer.com and saunablogger.cool websites! And of course the Planetcaver, and Planetskier blogs for other stories in Blogspot and TGR! The photos and text (c) 2021 by Jari Arkko. All rights reserved. I never take photos of other saunagoers or swimmers and try to visit at times where there is simply no one else around or the facility has been booked only for me.