According to the film's director the kids not only survived but thrived. Somehow, despite the fact this is well below the minimum viable population, they were able to repopulate the Earth.
Q. That's what's so scary! And it takes so long for the train to blow up! There is ... nobody left!
Bong Joon-Ho: I don't think Nam is an anarchist though. He just wanted to blow up one train car. It's the avalanche that kills everyone else. It's the
revenge of nature, if you will. Also, avalanches are most prevalent in
March or April, when the snow is slightly softer, just like in Nam's
dialogue. That's when avalanches happen, usually. Yes, they're all
dead, and that's a bit harsh. But it's a sci-fi film: If you can't say
these things, or have these ideas in a sci-fi film, where can you?
The idea of there being multiple generations of people on this train is a key one. There's an expression in the film: "train baby." Those
are the two kids that survive, the ones that only knew life on the
train. Someone like Curtis or Nam, they lived on Earth, then boarded
the train. These kids have never known what it was like to step on the
earth. So it's almost like Neil Armstrong touching down on the Moon
when they leave the train for the first time. They have no memory of
what it's like to be on the Earth. For them to procreate, it's going
to take a little time. So, for me, it's a very hopeful ending. But
of course there are so many deaths, and so many sacrifices ... it's
not so sweet. But those two kids will spread the human race.
Director Bong Joon-ho Breaks Down Snowpiercer��s Ending
No explanation is given how they managed it, other than that it's not as cold as previously imagined.
