I don't know how this affects bikes, but temperature does matter for cars in snow. In places that get below freezing for long periods, the ground freezes, and snow that lands on the ground stays snow. You end up with a snow layer on top of the ground.

In places where it gets cold enough to snow, but doesn't stay cold enough long enough for the ground to freeze, the snow near the ground can melt and then freeze as more snow lands on top, leaving you with an ice sheet between the snow layer and the ground. That can be much more treacherous to drive on, and I'd guess to cycle on.