Not all places have cold water during summer (did the greedy water company already run a heat exchange there?)

This would work but don’t use a conventional central heating radiator system: moisture would condense on the radiators and pipes, potentially causing wet floors and walls, and eventually mold. A radiator that deals with moisture well is an indoor AC unit, plus it has a fan, thermostat and remote control, and presumably they’re cheap to get when the more complicated outdoor unit fails. Just pump water through the coolant pipes! The water mains pressure is probably enough. (Don’t get an overly smart one or it will complain about lack of communication with the outdoor unit. Or hack it if you’re good at that.)

Alternatively, an air-to-water heat exchanger (heat pump whose condenser is submerged and evaporator is a conventional indoor AC unit) is way more practical. With cold water, it will use very little electricity and has all the convenience of AC. The output water can be used as preheated feed into your boiler.