"The Cross of Snow" is an elegy. An elegy is a piece of writing, often a poem, or a song, whose purpose is to lament and mourn the dead.
In this poem Longfellow is mourning his wife, who died tragically after an ember from the chimney that was in the room where the couple rested accidentally caught her dress on fire, burning her terribly. Longfellow himself tried to aid his wife to no avail, and resulting in the permanent disfigurement of his face, which was often concealed by his long beard. A death by fire is so horrifying that even in the dark ages those condemned to die by it would have committed the worse crime in order to get the worse punishment. Moreover, Mrs. Longfellow kept alive four days after her burning incident. Undoubtedly those must have been the most terrible four days in both hers and Longfellow's lives.
At the beginning of the poem, the winter atmosphere of coldness and isolation give the poem true Gothic qualities. The actual "cross of snow" that the poem refers to is the wooden cross build by Longfellow as a memorial to his wife.
That, sun-defying, in its deep ravines
Displays a cross of snow upon its side.
Such is the cross I wear upon my breast
He compares his wife to a martyr, for martyrs are also known for sacrificing their lives at the pillory. Her soul, he says, was noble enough to be considered a martyr in her own right. Her death was untimely, as death always is, but the particular cruelty of hers was entirely undeserving. This is basically what Longfellow says in this poem, which is one of the most heart-felt he has ever written.