How do I get the xbox series x/s version of Cold war?

Hi,

You have to pick up from the store the cross-gen edition and it will cost you the difference between the standard and the cross-gen version (around 10 bucks) :

How to upgrade Cold War from Xbox One to Xbox Series X/S

From what I can tell, to access the Series X version of the game, you need the Cross-Gen bundle...once you buy that, you should then be able to download and install the Series X version. Without the cross-gen bundle it will, presumably, just install the XB1 version

From the Store page:

"For digital owners of the Call of Duty®: Black Ops Cold War Standard Edition, this upgrade will unlock the Call of Duty®: Black Ops Cold War Cross-Gen Bundle, giving access to the Xbox Series X|S version of the game. After upgrade purchase, search in the Xbox store for the Call of Duty®: Black Ops Cold War - Cross-Gen Bundle to install the Xbox Series X|S version of the game."

Yes. Xbox One games will be backwards compatible with the Series S/X. There are also games like Valhalla and Cold War that support Smart Delivery. With Smart Delivery, you can buy the games now on the One and you'll be able to download the Series S/X version
for free.

Does the ultimate cold war version not work on the Xbox one?? Is it only for the series X?

I currently have the Xbox One S and the standard edition of Cold War installed. In a few weeks I’m going to get the Xbox Series S and I was wondering if I have to buy the Next gen version for Cold War at it’s full price.

Thank you

No you don't just buy the cross gen bundle for 10$