I don't know about the hot and cold things. I mean - some Chinese friends/visitors still ask for hot water on a hot day. I keep on hearing claims that hot water helps with digestion, even though the body self-regulates internal temperatures unless there's hypothermia or hyperthermia. The talk about ice water congealing fats is just silly because that doesn't happen in the body. Also - I don't think that's really a Chinese tradition per se but more of a tradition of boiling water to make it safe to drink. They don't have any such tradition in Taiwan, even before they had sanitary municipal water. Most homes would have boiled water that was then cooled or even used to make ice.
There have been studies that suggest that the heavy consumption of hot water has led to various cancers of the mouth and esophagus.
The big thing was that it made bland foods more interesting, and at a much cheaper price than traditional spices.
It is a Mainland thing, this video has the answer.