The cold weather will not affect the fermentation of yogurt if the milk is not heated.

The milk for making yogurt should be heated and cooled before adding bacteria. Adding bacteria directly to hot milk will burn them to death. Bagged milk does not need heating. Cold weather has an effect on making yogurt, and it takes a long time to ferment well. It is best to put some hot water in the yogurt machine (outside the milk cup) when cooking.