I can't link anything because i'm thick but if you enter something like "ideal temperature range for aquarium bacteria" you'll get a load of interesting stuff. Basically there is a temperature sweetspot where BB will thrive. As the temperature moves from this sweetspot, up or down, you'll get a reduction in BB activity.
A coldwater set up, especially an outside one, depending where you are, will certainly have reduced BB activity. It's well worth a read because it also goes into other aquarium parameters which also have an effect on BB activity, such as ph.