Dumb question, why is the water in the Rhine warm?
Doing that takes energy, that’s why it is called a heat pump. That moves heat from the water to an already warmer place, against a heat gradient, just as a water pump moves water against a gravity gradient.
If the water were warmer than your typical living space, they wouldn’t need a heat pump; a water pump to pump the water closer to where heat is needed would be sufficient.
And normal water takes quite a bit of heat extraction to actually freeze if at 0C, maybe the device does not even extract enough. But you want to be on the safe side of course since clogging up your heat exchanger with ice (which expands) is not great.
(edit: and as noted in other reply pressure is a thing)
Why do I have a feeling this is one of those "green" ideas that has some horrible environmental consequence. One that could have been solved with a way simpler technology for far less money in exchange for a bit of efficiency loss.
To be honest, I'm writing this comment mainly to say: what a great user handle, I smiled :-)
Ground source heat pumps are limited because the ground they have chilled stays stubbornly in the same place, so the only way you can extract more heat from it is to make it even colder, which gets less efficient. Watercourses don;t have that problem.
Not always good for the local ecosystem without mitigation, but at least one Japanese reactor allowed local colonisation by tropical fish and local legend said the same about Sizewell.
Sizewell C claims to plan recover waste heat and use it for carbon capture somehow, about which all I can say is a big old hmmmmm.
Not quite the same thing, but there is a tropical greenhouse in the south of France that used to be heated by cooling water from a nearby uranium enrichment facility: https://fr.wikipedia.org/wiki/La_ferme_aux_crocodiles (unfortunately not available in English).
You could get an even better result using the earth itself, but that is way harder to scale.
The air is colder in winter than the water, and the ground only provides a limited amount of heat before you can't extract any more. So water beats both.
And if it was really warm enough you wouldn't need heating in the first place.