I've visited hot springs dozens of times, but one experience was by far the best. I stayed at a 400 year old onsen hotel in late winter(feb) with a private bath on the balcony overseeing a river in the mountains. The loud white noise of the river, the terrible insulation and sleeping on the floor made the night not the most comfortable. But when I woke up early and went to the balcony I tested the water with my feet.…
Similarly, a bath in a balcony in the mountains is one of the best experiences of my life.
There was a continuous flow of hot spring water into the large square bath, big enough for two or three people.
As you say, the contrast of the cold mountain air and the hot bath with amazing views is just fantastic.