I've found the discomfort with near-freezing water in our cold-water-supply-only bidet seat to be minimal. Sure, I'd prefer warmer water, but it's really not that bad.
Isn't that why they have warm water ones?
Doesn't help much given how water's heat of evaporation is.
If that were true, wouldn't showering in those climates be much more uncomfortable? It's not like the water goes everywhere, or you don't dry immediately with paper...
If you ever took a hot shower in southern China in the winter without the benefit of indoor heat, ya, it’s uncomfortable.