Stacking Templates

[Joey Virtue]

So if I have a monster and I give them two templates one template gives it Vulnerability to cold and another template gives it immunity to cold what does the monster have

Example

Burning Skeleton and Skeleton Champion

So what is the monster after that in regards to cold damage?

[Bizbag]

They'd be immune to cold. Technically, they'd have both qualities, but the 50% extra damage is still reduced to 0.

Edit: note that technically your combination is not allowed by RAW, as the SC template cannot be applied to an undead. Not that doing so bothers me, but there it is.

The first answer to your question is still valid. A skeletal champion red dragon would be immune to cold.

[Joey Virtue]

They Burning Skeleton Champion is right out of a Paizo product

[Bizbag]

Ah, excuse me- the PRD does say that skeletal templates can be stacked. No matter; it was an aside anyway. Your main question was re: cold, and that answer is the same.

[Joey Virtue]

Yet in Paizo's write up it says weakness Vulnerability to Cold
But by what I have read you are correct.