well the point of cold war 2 will be to make sure your ideology has the strongest influence
expanding your influence can be done in a number of ways, such as installing puppet regimes/indoctrinating other nations to your ideology, displaying the power of your ideology through technological demonstration eg rocket launches, winning proxy wars against opposing ideologies, supporting rebels in foreign nations, etc
warfare really won't be a huge aspect of cold war 2
just in proxy, not so much in nuclear