In the United States, most people plant at Memorial Day - usually geraniums. But by mid-summer, they're either dried out (if families plant and just hope there is enough rain!) or what my mom calls "get leggy", that is, long stems with not too many flowers at the end.
In reality, with just a little effort any grave site can look terrific in every season. Those Memorial Day flowers can be pulled up and replaced with colorful pansies or hardy begonias for the summer, followed by yellow, purple or white mums in autumn. Winter hits hard in the northern climates, but can start with with white and red geraniums, or a spray of evergreens.
Also consider whether you want to place a basket of flowers to commemorate a birthday, or perhaps sprinkle candy corn on Halloween. Maintaining your loved one's grave site through the year keeps it neat and ready to receive the next special arrangement, whether June or November.