Are you talking about a fantasy/sci fi project, or about what would happen? If you talk about a fantasy scenario, then yes, you might be right. If you talk about the real world and a small nuclear war (only major cities of the main opponents nuked), then the earth would change nonetheless because of all the radiation that knows no borders and goes wher the wind goes. Do you know about Chernobyl and how the children in Europe played inside that summer? There would be lot of radiation everywhere on the planet, making live for every higher liveform than grasses and cockroaches difficult. Even in areas where there had been no nuclear strike, many people would die of cancer and many children would be born with horrible changes. Even if the athmosphere would not be entirely messed up.