The speaker in this poem is a bereaved father. For the first several stanzas, the poem simply describes the wintry scene, but it is clear that the snowfall makes the speaker think of another place where snow is falling—upon the grave of his child, with its "little headstone."

The speaker remembers his daughter—his living daughter, Mabel—asking him where snow came from; he responded that God makes it snow, as he makes everything. Lowell then uses a metaphor to compare the falling of snow to the way the passage of time makes it easier to bear the grief of loss, although it never really goes away. Just as snow blankets the landscape, a gift from God which covers up blemishes and imperfections and makes everything appear smooth and clean, time too begins to blanket over pain flake by flake until, eventually, life seems bearable again.

James Russell Lowell uses the imagery of the falling snow to reflect on his child's death in his poem "The First Snowfall."   Lowell uses details from the poem, such as the "little headstone" being blanketed in the snow as "did robins the babes in the wood."  The speaker's diction choices, especially "little headstone," allude to the fact that a child has died. 

In stanza seven, the speaker reveals more about his loss, because watching the first snow fall reminds him of his "first great sorrow when that mound was heaped so high."  He looks at the new falling snow and remembers the day of his child's funeral; "the mound" refers to the burial mound.  He compares the falling snow flakes to his gradual acceptance of his loss amidst his grief. 

In the final stanza, when he kisses his other daughter, Mabel, and thinks of her little sister who has died, this action is the speaker's way of making an emotional connection to his daughter who has passed away. 

In "The First Snow Fall" by Lowell, how do we know what happened to the speaker?

The speaker's daughter has died, she must have died recently, and been very young.  We know because he describes the beauty of the snowfall and talks about "a little headstone" (line 18), our "first great sorrow"(line 27), and the fact that it is the first snowfall (title) that hides "the scar that renew(s) our woe" (line 32).  In the latter part of the poem the speaker is addressing another daughter, "our little Mabel" (line 21). It is her sister who has died and is now "folded close under deepening snow" (lines 38-9).