If the batteries are cold, as in sat out overnight cold, you will see reduced power & shorter range, perhaps 50% or less of summertime, depending on temperatures. This generally is not permanent, and the batteries will bounce back in the warm weather. Lead-acid will be much more prone to this than Lithium, but Lithium will still experience it to a degree.
If you cannot bring the bike in out of the cold, then consider any arrangement that allows you to unstrap the batteries and take them inside. It takes several hours for batteries to acclimate going from warm to cold, and they generate internal heat when being used, so an hour or so of use out in the cold will not reveal too much performance degradation.