Frost shows up in the beginning, and then… it shows up in the end. But, by the time we see it again, we understand what it really means (or, we're supposed to). Coleridge's poem is centered around finding meaning in Nature—and that includes things that might be a little cold and not warm and fuzzy. Yet, they express beauty and divinity, just as well as the things that are warm and fuzzy. The poem centers on Coleridge's hope that his baby son, Hartley, will learn to find joy in all natural things and seasons—including the frost, which becomes the primary symbol for the evidence of God hidden in a secret place.
Lines 1-2: At the beginning, the frost is just frost, doing its frosty thang: freezing stuff. Most people probably wouldn't say "Oh, man, I love frost. I can't wait for it to frost!" the way they might say, "Sunsets are lovely!" or "The ocean is nice!" So, when frost appears, our attitude towards is supposed to be a little indifferent or ambivalent or confused. What does it mean that it's performing its "secret ministry," anyway?
Lines 71-75: By the time Coleridge has described how Nature is God's "eternal language," we start to get the true meaning of the frost. At the end, it shows up performing its "secret ministry" again, creating icicles, and we're supposed to realize that the frost is a "minister" because it, like the rest of Nature, it's an agent of God. It testifies to his existence. By creating icicles that reflect the moon back to the moon, the frost is like a poet who becomes inspired by the presence of God in Nature and tries to reflect God's glory back at him, by creating poems. Everything in Nature, says Coleridge, symbolizes this divine creative process.