Some say the world will end in fire, (line 1)
The speaker functions like a judge evaluating two arguments. At the beginning of the poem, we do not yet know whether he will weigh in on the debate.
Some say in ice. (line 2)
Oh, it's on. "Fire" and "ice" are pretty arbitrary phenomena, as far as ways to end the world. Why only these two? What about being sucked into a giant black hole? Giant Godzilla attack? (OK, so you can probably file that under "fire.") The point is that Frost doesn't care about being strictly accurate; he is setting up two contrasting symbols.
I hold with (line 4)
The speaker uses a very legalistic phrase to let us know that he's planning to take sides in the argument. He sounds like he's competing at a high school debate tournament.