Grass covers the majority of the player's town. In early December, snow falls and replaces all of the town's grass. On February, 25th, the snow melts, and the grass comes back. In September, the grass begins to become lighter, then turns darker and browner in October and November.
Grass by game
In Animal Crossing, all of the town not occupied by pavement or buildings was filled up with grass. There were only a few spots occupied by dirt, and those were designed in figure 8-like shapes.
In Wild World, more of the land was occupied by dirt rather than grass, giving the player's town a more desert-like feel.
In City Folk, the player starts out with an almost complete town of grass. However, as the player plays the game, the grass starts to disappear. This process is called grass deterioration, this process only happens in areas where the player walks (and usually walks/runs most often). Grass will wither faster if it is run over rather than walked. However, grass deterioration can be prevented by staying off dirt where the player would like grass to regrow in. This process can take up to a few months until the grass regrows completely.
In New Leaf, grass deteriorates the same way as in City Folk, but at a slower pace. Grass deterioration is not prevented by placing a pattern over it. Grass can be regrown over dirt by planting flowers over it, and watering those flowers every day (even if the flowers are not dying) until the grass has regrown completely. Rain and snow will also accelerate grass restoration.
In New Horizons, grass no longer deteriorates due to the ability to customize terrain however the player wishes. Additionally, different grass shapes no longer exist and all islands will always utilize the triangle pattern.
There are three different designs for snow/grass in the Animal Crossing series. The patterns change when grass turns to snow and vice-versa. (The picture below does not apply to New Leaf and New Horizons.)