To get an exact answer to whether your neighbor can stop you or not from planting trees, you need to check the exact rules and regulations of your local area.
However, generally speaking, your neighbor doesn’t have a say on what you do or do not do within the boundaries of your property, and that includes planting trees. Even if it might look as though the roots of the tree could expand into your neighbor’s house, they will still have a hard job at trying to stop you, because you are planting them within your designated area.