Once a long time ago, I would have agreed with you. Snow produced from a frontal movement often happens when the temperature has warmed a bit. But I have learned that lake effect snow happens in extreme cold and has the characteristics of fine snow rather than big flakes once it sets up. I suppose it doesn't have to be small flakes but seems that is what it usually shows up as, and can still dump a significant snow-fall on your head....all the while never getting above zero degrees F.
I remember this happening for 7 days straight
...snowing constantly at various intensities...never quite stopping completely but at times you couldn't see 20 feet.