Anic, most koi/goldfish aren't fed during the winter, except if your relatives' fish would be in the tropics. Their metabolism slows down during the colder months, and everything that is in their bodies and not being processed, will rot and cause trouble big time.
My fish don't get anything to eat once the pond temps hit 55, and they do just fine that way.
The fish inside - if there is no heater in the tank, and the temperature drops to the lower room temperature, yes, fish will know and adjust accordingly with less mobility and less appetite.