In Fog of War buildings do not show the color of their owner unless in vision of your units. A player must especially keep this in mind for cities as they are usually the most abundant building as well as being heavily fought over. It is a significant advantage if you can predict what cities your opponent could have captured when temporarily repelled from a part of the map. It also provides you with a way to make a rough estimate of how high the income of your enemy is.
In Advance Wars: Days of Ruin (Dark Conflict for non-Americans), cities, like all properties, allow you to see up to 2 squares away.