I can't imagine a mechanism whereby the cold would affect an Infinity connection. I don't know how much heat is dissipated inside the Cabinet (it has fans so there must be some to get rid of), so it should be nice and warm inside. If some of the electronics is on the edge, I suppose it might pose a problem, but it's usually heat and not cold that electronics dislikes (eg, the vdsl Modem problem).
I have noticed some recent variation in speed, mine dropping to around 25Mbps from a usually stable and consistant 32Mbps.
As I use a tool similar to tbbMeter to monitor my instantaneous connection speed, I have noticed that its display gets spikey from time to time. If you do a test involving a large transfer of data (like the BT Speed Test) the spikes get averaged out.
However, it you use a short test and you hit some spikes, then a lower speed gets reported.
This tester is a short one and if you run it several times in quick sucession you may see quite a variation in speeds being reported.
http://www.speedtest.bbmax.co.uk/
Might be something to consider.