The speaker opens the poem by directly addressing someone who has died and is now buried deep in the ground, under a heavy pile of snow. This other person obviously cannot respond, making this an example of apostrophe. (Note that this guide is treating the speaker as female and her deceased beloved as male, in keeping with the original context of the poem as being told from the perspective of a fictional queen mourning the death of her husband. Keep in mind throughout that it's possible to read the poem differently; more on that in the Speaker section.)
"Cold" is an important word here. It is a term often associated with death (whereas life connotes vitality and warmth). The beloved's body is literally cold in that it no longer has warm blood flowing through its veins and is surrounded by the cold winter ground. Indeed, this person's grave is buried under a deep layer of snow, the sheer weight of which is evoked by the phrase "piled above." "Cold" can also have a more figurative connotation of loneliness, of being without love, which is also being evoked here.
The repetition of “cold”—which both opens the poem and begins the last clause of this sentence—thus emphasizes the harsh reality of death, an emphasis heightened by the speaker’s imagining of this person's "dreary"—or dull, depressing—"grave."
The epizeuxis of “Far, far removed,” meanwhile, underscores just how far away the person who has died feels to the speaker. All in all, these first two lines thus hammer home the intense separation the speaker might reasonably feel from the beloved, who seems utterly beyond her reach. The assonance of long /ee/ sounds in “deep,” “thee,” and “dreary” further connects this beloved (that "thee") to the "deep" and "dreary" reality of death.
At the same time, these lines establish the emotional crisis the speaker is undergoing. While acknowledging the physical reality of death, and how far away her dead lover feels, the speaker addresses her beloved directly as “thee.” This direct address gives the lines a sense of intimacy, as though the person who has died is still right there with the speaker. Within the context of the rest of these lines, which emphasize that the person who died is “cold” and “removed,” the direct address builds a crucial tension into the poem at the outset.