From what I’ve gathered, water based heating systems pump around hot water, not steam. Otherwise, the radiators, which are easily touchable by anyone, would be insanely hot, and thus a significant fire and injury risk.

In order to use them for cooling, I suppose you’re going to need a different transport medium, i.e. something like glycol instead of water. This would make the system harder and potentially a bit more dangerous to maintain, limits power when heating (water has higher specific heat than glycol), and you’re still stuck dealing with condensation at the radiators.

Using an air system for centralised cooling works. Using a water system is much more problematic.