What gets a cold front moving?

"Cold fronts represent the forward moving boundary of cold air that is wrapping down toward the equator behind the Low, eventually wrapping around the Low. " Are you saying that, the Lows tend to pull the Cold Airmass and Front down from the higher/colder longitudes? The cold air mass would initially be "above"/poleward, then behind, then "below" as it gets wrapped around the low, secondary to the Coriolis Effect? That would help me understand the inevitable linkage of those two very different, but often hand-in-hand, wx phenomena.