If people that repeat this claim, asserting it as fact, don't have citations -- then that's a different but related problem.
In Australia we got this under control through winter. Several states (South Australia, Western Australia, Tasmania, Northern Territory) had it so well controlled they had little if anything resembling strict lockdowns. Also through winter.
If 'all of Europe' (I'm not sure if you're talking mainland only there, or are including the very warm bits down the south, etc) is having the same results, then absent a control set to compare to, we can't know if that's an effect of comparable politics / culture, lack of controlled border controls, that a tipping point has been reached, or, as you say, 'because it's cold'.