This question is answered by Syd Mitchell, after the break...

The bacteria in a freshwater tropical fish tank filter are the same as those in a koi pond biofilter, (nitrosomonas & nitrobacter), but in winter, trying to seed the pond filter with their cousins from a tropical tank will not help.

In winter, the koi pond’s biofilter bugs are either dormant or have a very low metabolic rate, waiting for warmer weather. As the water warms, they slowly increase their metabolic rate and begin to remove ammonia (and nitrite) and use it as an energy source just as they did the previous summer, but they will only do this at a rate that is controlled by the water temperature. If the tropical fish tank is in the usual temperature range of 20^oC or higher, the filter bugs will be active in its filter, but as soon as they are put into the cold water of a koi pond biofilter in winter, they too will become dormant.  Bug activity is dependent on temperature so feeding fish very sparingly with low protein food until the water is warm enough for the bugs to have recovered their full colony size and efficiency is the best way to avoid what is usually known as “new pond syndrome” which simply means that the fish are producing ammonia faster than the bugs can "eat" it.