Good question. You must pay attention to the messages you get after a mission that you succeed / fail as well as the occupation situation on the global map. Your objective is to push the Soviets back, out of Europe. At some point you get a 'special' final mission (I don't spoil it here) which is different than others. Succeed this one and you - most likely - will win the war and the campaign.
Fail more contact missions and you will step back in the campaign, eventually the Soviets will regain control of the waters and re-occupy European territory, and you are go to make again several successful missions before getting back on track. Again, messages with pictures will inform you about this, the messages will be the same at some point.
In Red Storm Rising it was easier to judge because there was a 'progress bar' showing the war status, but not so in Cold Waters. This makes it more of a suspense I think
[EDIT]
To know EXACTLY, just analyse the 'event' triggers in campaign_data.txt.