Why cold specifically, and not just 'winter' in general
It's worth distinguishing a gradual seasonal cooling from an actual cold snap, because the biology responds differently to each. A slow decline in temperature over weeks gives rodents and insects time to adjust behavior gradually — some insects finish moving into harborage before the first hard freeze even arrives, following typical fall patterns extension sources document well. A sharp, sudden cold snap compresses that same behavioral pressure into a much shorter window: outdoor food and shelter options that were marginal suddenly become untenable all at once, and animals already close to a structure move decisively rather than gradually.
This is the honest mechanism behind the common homeowner experience of 'we didn't have mice all fall, and then it got cold for a few days and suddenly we did.' The mice were very likely already in the general vicinity; the cold snap is what pushed the final move indoors.

