The Sages’ enactment against using trees applies to shrubs and vines that have hard branches or yield hard fruit, like pumpkins. However, the enactment does not include soft weeds, bushes, or branches. Therefore, one may sit on a lawn on Shabbat, even if it moves the grass slightly.
One may not smell an edible fruit while it is attached to its tree, lest one end up plucking the fruit in order to eat it. However, one may smell fragrant flowers where they grow. This is because he has no reason to pick them, as they can be smelled while still attached to the ground. If tree branches themselves are fragrant, one may not grasp them and move them closer to smell them, because one may not move them, just as one may not move a tree. If the branches are soft and pliant, as are myrtle branches, one may grasp them and move them closer to smell them. One must, of course, be careful not to pluck the branches.
One may walk on a lawn even though walking on it may uproot some grass. This is because he does not intend to do this, and it is not necessarily going to happen. But if the grass is high and it is certain that walking on it will cause some of it to be torn up, one may not walk on it (SA 336:3; BHL ad loc.).
Not only did the Sages prohibit using a tree, they also prohibited riding on an animal, lest the rider break a branch to use as a riding crop to direct the animal. The Sages also prohibited extracting honey from honeycombs, because this resembles picking produce (SA 321:13).
One may bring his animals to a grassy area so that they may graze. This is not considered Kotzer because the animals are eating for themselves. We are not commanded to ensure that animals keep Shabbat; we simply must ensure that they do not perform melakhot on our behalf (Shabbat 122a; SA 324:13).