There's been a lot of argument over hot vs. cold bathing throughout history in the Western world. Public baths, whether in the Roman period or their rebirth in the 18th century, tended to be warm water based. The Greeks argued for cold bathing, imagining a tougher, stronger person would result from less soft indulgence. A belief seen again and again through history. Edward Gibbon in the 18th century believed that hot baths were a large part of why the Roman Empire fell. In 1701 Sir John Floyer published "The History of Cold Bathing" which not only contained stories about those that bathed in cold water, but a multitude of amazing cures that came from it. Most claims were far beyond possible, things like curing the lame or consumptive.

Over the next couple of centuries cold water was claimed to solve everything from lust to a greedy appetite. The Victorian emphasis on good, hard work brought about arguments that cold water could change anyone, no matter how lowly and dirty, into a model citizen. Charles Kingsley's "The Water Babies" written in 1863 is a perfect example of this; Tom, a young chimney sweep has a transformation when he comes across a young girl bathing and realizes his own filth. Outside of the claimed benefits, cold water was just more available until very recently. Even when hot running water was installed, it often produced filthy cold water instead, taking quite a while before all of the kinks were worked out of the installation process.

For the most part, the claimed benefits of cold water were either nearly impossible health cures or rooted in the belief that warm water was best left to the infirm, fragile, and effeminate. There were certainly some realistic claims to health in these arguments as well, but they tend to be downplayed next to some of the grander ideas. I really recommend reading The Dirt on Clean by Katherine Ashenberg. She goes into good detail about the history of bathing and cold v. warm comes up over and over.