It's a curious thought of "could you close a room and point a fan at it and noticeably cool off a room?"
This would be kind of running a mini-split AC to the rooms using water as the refrigerant instead of what hvac normally runs.
It's not a "this is the best choice" or even "this is a better choice than opening the windows" but rather a "if you did this, would it work? kind of?"
Theoretically you could indeed drive cool water to the radiators to cool the house, but you don't get the convection effect that a radiator produces when hot, nor thermal radiation. So you need to rely on transfer of heat from the air to the metal of the radiator, potentially with no airflow. Easier to open the windows. In the last 12 years, I've never wished I had a system to chill the air in my dwelling; Ireland is generally on the cool side (though this may change).