my favorite subject!
I guess we get so caught up in talking about nitrifying bacteria that we forget the bigger image of the bacterial survival family ( of which nitrifiers are card carrying members!).
Bacteria is the first to be here and the last one that will go. The highly adaptive nature of bacteria is far beyond the capabilities of any fish or mammal that we know. Bacteria has adapted to living in icy waters of the arctic, boiling waters of geysers and volcanic vents at the bottom of the ocean.
Scientists divide bacteria up in groups under all kinds of criteria. Some according to the temperatures they live at, some according to the 'food nutrient they use' and others according to how they make energy.
If we look at nitrifiers in terms of the temperature group they fall in, they are psychrophilic organisms ( 60 F- 77F) compared to mesophiles of the soil bacterias that prefer warmer temps in the 77- 100 F range. This is why some of the data on 'fish tank' bacteria is actually wrong in that it took it's impression of bacteria from studies in soil dwelling nitrifiers. No terribly wrong, but slightly misleading.
Here is a very important point-- these temperature ranges are for meant to denote where a bacteria grows best. This is not always where a cell is most efficient at. This would be semantics to a scientist but all important to a hobbyist. It has been proven that efficiency is at it's peak very close to the limits of temperatures for growth. In otherwords, temperatures that are so high that they supress growth due to effects on certain proteins, have the cells working the 'hardest' in terms of hobbyist's perspective.
On the other end of the scale, cooler temperatures slow metabolism in nitrifiers. But they are adaptable. This is why an established filter is such a valuable thing. Your bacteria are adapted to seasonal change. Not unlike a bacterial population that 'learns' about antibiotics and how to dealer with them, a population adapts to other conditions within it's survival range.
So there are two issues here- the survival of a cell and the growth of a bacterial population. Our bacterial populations do not grow in water below 50 F. And if conditions are too challenging ( IE no circulation, no ammonia, no oxygen, excess die off rate) they stress and die. But if only water temperature is changed/ lowered, you get :
1) no population growth
2) survival techniques
3) adaptation
depending on the condition, age and circumstances, you will have low level activity, sloughing and survival.
As someone mentioned, the fish and the entire system slow in metabolic production as water cools. And the bacteria is no exception. It is in sync with the environment. As food source declines, growth declines. And death rates, of course, are a constant regardless of temperature. So the population atrophies as much as dies back. No new ones, survival of the young cells and death in the old cells. But a typical winter sees an adapted core population and things called 'resting cells' surviving to next spring with minimal ammonia and minimal activity.
So don't shut off the filters! This will produce a highly refined and adaptable population to your specific conditions.