How does the poet use symbolism to represent a shift in the speaker's attitude?

Throughout the poem, Longfellow uses descriptions of the weather conditions—"The day is cold, and dark, and dreary," for example—to symbolize the speaker's sorrowful and sad frame of mind. It is raining, the wind blows, and the dead leaves fall from the trees, and these negative descriptions parallel how the narrator feels about his life; he cannot stop thinking about the long-dead past, and he realizes that all of his youthful hope is gone. However, in the third stanza, there is a shift into something more like optimism. He says,

Be still, sad heart, and cease repining;Behind the clouds is the sun still shining;Thy fate is the common fate of all,Into each life some rain must fall,Some days must be dark and dreary.

In other words, the rain still symbolizes sadness or sorrow, but behind the clouds, he says that the sun is still there. The sun seems to symbolize hope, and the happy times that will inevitably be interspersed with the "dark and dreary" days. Thus, the final stanza achieves a hopefulness that the first two stanzas lack. Yes, we must accept some sad times, but we will have happy times too.