Why are they on a train in Snowpiercer?

The train had been designed before the global disaster for luxury travel through all climate zones of Earth, including the arctic tundra. It had a long-term power source and the ability to produce (some) food. The paying guests would get fresh sushi, not food out of a freezer.

In the real world, rail lines are only electrified if there is high traffic. On secondary lines the engines have onboard power generation, usually diesel engines. It seems logical that one tourist train does not constitute "high traffic" and that the lines were not electrified. Why the engine did not use diesel fuel is not answered, but perhaps the logistics of refueling depots would have been impractical.

When the disaster struck, the number of occupants was increased and steps were taken for complete self-sufficiency. These steps were not completely successful and the situation is slowly deteriorating, but obviously the biomass recycling is quite efficient. Why the train would move instead of parking in a relatively warm spot is an interesting question.

Political power and mental instability:

As long as the train is moving, the elite in the front cars have the advantage over the tail and the train engineer Wilford has the absolute power over everyone in the train. If the train would stop, even if it would still be used as a shelter or energy source, his power would diminish as people could either find an alternative to his train or get more bold in attempts to take over the forward cars: When the train is running, the avenue of attack is just a narrow, easy to defend corridor, when the train is stationary, the cars (and engine) can be surrounded.

Please note how much Wilford is worshiped:

Let us go to a special comment from Mr. Wilford, the Divine Keeper of the Sacred Engine...

Engine yo aei en ni! Wilford Ban zai!

The Engine is Sacred and Wilford Divine...[...] Wilford is merciful...

It is not hard to imagine that such worship would unhinge the already eccentric Wilford. Even while in the end he is willing to give up the power, he believes that his ways are the only correct ones.

I think that ample information is given in the film as to why the last of humanity all live on one giant self contained train the world is frozen completely wiping out life on earth. There are a group of survivors living on a train and as long as the train is moving it’s engine provides heat, water (in the form of melted snow and ice) food with the aquarium etc.

During the film it’s shown to an extent that Wilford built the train and engines to be a luxurious cruise liner type vehicle then there was a world wide disaster and the train becomes home to the last of humanity. There’s a clear class distinction where first class passengers ~ that have paid the most to be aboard the train~ live in luxury then another standard class of passenger live in less luxury and the rest of humanity are allowed to live in the tail sections of the train for free therefore showing Wilford as a charitable man to a degree (no pun intended) it makes sense that they are on a train as the engine is some form of perpetual motion machine that endlessly circles the globe ie motion means power and heat allowing it to be a self contained environment.

I think out of the many end of the world apocalypse type films Snowpiercer gives a good account of itself in explaining how and why the train works and why everyone is on a train in the first place throughout it gives explication of why things are the way they are even down to the protein blocks fed to the passengers at the back being made from cockroaches and other bugs. In a true life book I read about an Australian guy who was sent prison in Thailand the Thais eat crushed up cockroaches and other bugs to compliment the meagre rations they are given, so even the idea of the protein blocks has some substance to it.

The only thing that the film fails to acknowledge is that there most likely would be other people living in settlements around the world perhaps underground or finding heat sources from elsewhere but on the whole Snowpiercer explains itself and the reasons that the last of humanity clings to life onboard a huge train quite well and viewed from the point that the tail end passengers travel for free but still have food and water Wilford could be viewed as a saviour of the human race hence why he is almost worshiped by those that work on the train..

The film doesn’t actually need to explain this satisfactorily why the train has to keep moving, because the film doesn’t really say it does; the characters in it from whom the claim originates are established as unreliable or untrustworthy.

Focusing on the technicalities of what about the train makes it the Ark or what else might serve as such is losing sight of the simple fact that the train and everything about how it works and what it’s doing is by Wilford’s design.

The simplest answer for “why does the train have to keep moving” is: Wilford wants it to keep moving, or believes it must. Whether he’s right or wrong on this is secondary; the point of the movie is it’s his call to make regardless.

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I’ll concede up front this is somewhat circumstantial, but I’m convinced that at least part of the in-universe reason is the same as the thematical reason.

That is, while the stated objective benefits - energy generation and melting ice into drinking water - are true, the train does that and it’s an important function of the train, it is not absolutely certain the a moving train is the only option. (Especially as it’s revealed to actually not be a perfectly balanced and sustainable environment.) And the way it is presented as such should give one pause.

The evidence we have is:

• As I mentioned above, the train appears to be crumbling and will fall apart eventually.
• Meanwhile the outside is shown to not be unsurvivable. Polar bears are an apex predator; the existence of one, many years after the ice age began, implies the Earth can host its whole food chain.
• Wilford is a fanatic about the existing order, to the point of being a deific figure in a religion of sorts venerating the train. The factuality of claims about the train made by zealous believers should be taken with a grain of salt.
• Wilford also plays 7D revolution chess to maintain (his idea of) the equilibrium, manipulating events to vent social tension while culling population back to what he views is a sustainable level.
• The school scene where the children are made to chant along to something along the lines of “if we went outside we’d all die!” might as well be signposted This Is Propaganda.

So, the narrative that the train must keep moving is, I’d argue, a little dubious even in-universe. It comes from Wilford and his proxies, and Wilford is shown to be both a deceiver and rather unhinged; his ostensible concern for the survival of mankind is somewhat contradicted by his disregard for individual lives. (Those of the tailies in particular.)

I believe the above are hints that maybe it doesn’t! (Even as it’s a slim maybe, in the sense that the chances of survival without it are significantly worse.) And Wilford is painted as the sort of person that, confronting this possibility, would reject it, since his plan works better; lie about it to get people to stick to said plan; and end up in denial over and rationalize away his plan’s failings. (Or he just doesn’t care about the tailies to bother with something for their benefit.) Remember that he’s adamant the stratification and the deaths and suffering it brings are necessary; that he’s in first place is a happy coincidence of there being, to his mind, no other functional arrangement possible.

If you have doubts regarding the explanation given seeming flimsy, it’s because the explanation as given in the movie was supposed to seem as smoke and mirrors. And the “political” reasons - easier control of society - aren’t just interpretation of a metaphor.

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YMMV, I believe the story tells its message (of a broken system kept uhh… moving through ideology) better with this ambiguity in-place, if the “train must keep moving” isn’t a hard objective constraint serving merely as a convenient framing device.

In doing so, it serves not only to shine a light on the injustices of an inequal social order - and on the other hand, critique the revolutionary impulse, or the misguidedness of trying to right injustice by usurping institutions designed to impose it - but also to show that order as being arbitrary and the product of power. This whole arc is set up as a bait-and-switch, and in light of this, the train isn’t the only way for mankind to survive; it’s just the one a man with the power and resources to do so holds into place.