Cold air, wind shift, and high humidity all come with the cold front. The shift to easterly winds can push the fire back or keep it from progressing as far. If it blows back on itself, it may run out of fuel - side one of the fire triangle. The easterly winds will also be lighter than the westerlies that pushed it so far yesterday/today. Lighter winds = less oxygen, another side of the fire triangle. Cold and high humidity cool the fire, lessening the third side of the fire triangle - heat. Precipitation would cool it more, which a cold front can also deliver if it provides enough lift to push the air to a point that is cold enough that it saturates and rains/snows.
Basically, this cold front *should* be the 1-2 punch to suppress the fire, at least on this side of the divide. That is, if the fire isn't so fucking hot and raging that it creates its own weather.
I'm just an amateur dentist, but that's my weather take.
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