Leaves like the things of man, youWith your fresh thoughts care for, can you? (3-4)
Margaret is young and hasn't yet experienced much grief. Lucky her! So she's looking at the leaves with "fresh" eyes and with "fresh thoughts." She's sad just because the leaves are withering and falling. The speaker asks if she can care about the "leaves" as much as she can care about human concerns ("the things of man"). He poses it as a rhetorical question, but why do you think he phrases this as a question?
Ah! as the heart grows olderIt will come to such sights colderBy and by, […] (5-7)
The speaker says that, as Margaret gets older, she won't care as much about "such sights" as the falling of leaves in the autumn. He probably has a point—how many adults do you know who get all sniffly when a leaf drops? But to say that she will become "colder" puts a more negative spin on it. After all, no one wants to be described as "cold."
Now no matter, child, the name:Sorrow's springs are the same. (10-11)
The speaker says that her innocent sources of sadness ("sorrow's springs") are the same as they will be when she's an adult. It's just that when she's an adult she'll be able to label her emotions ("name" them) more effectively.