Symbolism, Imagery, Allegory
You'd think, what with the horrifically cold North Dakota winters wreaking havoc on everything in sight, that ice would be a top symbol. But nope: as far as Giants in the Earth is concerned, ice is just frozen water. Fire, on the other hand, is civilization, blind luck, and egotism.
When Per Hansa and his family set out for the Dakota Territory, they try their best to follow the trail that's been blazed by their Norwegian friends. But Per messes up his navigation and quickly loses the trail. The only thing that saves him is randomly stumbling on a fire that he knows must belong to his friends:
Yes, he was right—here there had been a fire! It couldn't have been many days ago, either; the smell of the ashes was still fresh… His eyes had grown so moist and dim that he had to wipe them…But he wasn't crying—no, not yet! (1.1.5.10)
At its core, fire is a symbol of humanity's struggle to harness nature and to survive in cruel places (like the prairie). It's a central image in almost all settler literature, but especially important in this book when we find out how brutal the Dakota winters can be.
Also, Per finding the fire-pit is the first in a long—unlike Lemony Snicket would have us believe—series of fortunate events for Mr. Hansa. His success on the prairie is part inspiration, part perspiration, and several billion parts dumb luck. He gets lost from his group as he's travelling to North Dakota… but lucks out and finds a fire-pit. He plants potato seeds too early in the season… but lucks out and they grow anyhow. He gets lost in a blizzard… but lucks out and finds his buddies.
But lets not overlook the root cause of all this luck. You usually don't just "get lucky." You have to have the ego and grit to take the leap that allows luck to happen. Most lottery winners have to feel pretty special ("I'm one in several million, woo-hoo!") in order to justify buying their winning ticket. In that same way, Per's ego is necessary for him to doggedly look for his comrades' fire-pit instead of admitting, "Welp, I'm lost," and turning around.