Get out the microscope, because we’re going through this poem line-by-line.
Ah! as the heart grows older
It will come to such sights colder
By and by, nor spare a sigh
- The speaker says that Margaret won't react with the same kind of sympathy when she gets older.
- Of course, it's not Margaret that's mentioned, but "the heart." This is just using a part of the body (where we tend to think that emotion lives) to represent the whole of the person and his or her attitude. That whole using-the-part-to-mean-the-whole trick? It's called synecdoche.
- In any case, what the speaker really means is that Margaret the person will, as she ages, become "colder" to "sights" like the leaves falling from trees.
- The speaker is probably right—after all, how many adults do you know who get all weepy-eyed every time they see a tree losing its leaves?