Bad information! If there is no danger of the filter freezing, it should not be shut down. Metabolism, albeit at a low rate, continues for all aquatic animals at low temperatures which means Ammonia is being produced. Even though it is considerably less toxic at low temperatures a high enough level of Total Ammonia (TAN) will produce enough un-ionized Ammonia (toxic form) to be lethal.
The only time that a fish does not produce Ammonia is when it is dead!
Agreed Meyer I have a canadian koi friend who regulary brings in her koi each year with no losses filters and airpumps as well .
Where did you get your information from
@James99 [the internet] ???? ... its far better to buy books on the twin subjects of the arts of fish keeping and the art of fish health and disease , study those books well because they may just save the lives of your koi .
This year will be our 30 year of koi keeping with hopefully many more to come , I have a large reference Library of Koi and fish health issues built up over the same period of tme ,
@James99 the point of this is that, I've found it most useful over the years !!!!........ as its given us many relaxing and peaceful years sitting by the pond helping out when an issue comes to the fore
See Article about it for titles ISBN numbers [where possible], lastly those all important authors names with a revue of each book :-
https://www.gardenpondforum.com/articles/our-updated-library-with-reviews.11/
This should help you out
Dave