Aside from the very clear use of rhyme, "Fire and Ice" seems rather formless. But there's a lot going on in those nine lines. In his early career, Frost stuck to more traditional forms, like rhyming couplets and iambic pentameter. He mastered them as well as any American poet ever has. So, when a great craftsman like Frost decides to loosen up a bit, as he did later in his career, you can still see bits and pieces of a more orderly style. You know the saying: you have to learn the rules in order to break them.
The rhyming is hit-you-over-the-head obvious. For example, in order to rhyme with "ice," you have to use words that contain "ice." And, in order to rhyme with the word "fire" you have to use words that contain "ire," a word that means "anger" or "wrath." So, Frost makes a very clever choice in repeating these sounds several times. In the deep pockets of your mind, they resonate with a primal drumbeat: "ice…ice…ice" and "ire…ire…ire." You sense the elemental quality of these emotions.
The first two lines are really like a prologue. They do not have the same rhythm or syllable count as the other lines. Starting in line 3, a pattern becomes clear: eight-syllable lines in an iambic meter. An iamb is a rhythmic unit with an unaccented syllable followed by an accented one: "I hold with those who fav-or fire." Most lines in the poem have four iambs. The last two lines are really like a single line that has been broken in two for the sake of the rhymes. It's as if the poet decided to make his rhymes work "double-time!" This quirky, unique ending accounts for much of the poem's fame and power.