If fighting breaks out in Europe or the Middle East then a full nuclear exchange is almost inevitable. It's possible that you might get direct exchanges taking place in proxy wars or in conflicts seen as strategically peripheral but the politics would become very difficult for either side to back down. On the other hand, they don't necessarily become so difficult for the 'change' power in the local scenario as to justify the severe risk of a full nuclear exchange. What would happen though if, say, the Soviets withdrew from some Africa post-colonial conflict that the Americans became engaged in (for sake of argument), is that the US would become much more assertive elsewhere, both in local theatres (some of which would have been of primary strategic interest to the USSR), and in direct bilateral relations.