To prevent the invading army from doing exactly that, the common tactic was to bring everyone and everything into fortresses, and then burn the rest and poison the water supply.
Not forcibly.
The Russians used that kind of "scorched earth" technique much later than medieval period (safe the water poisoninig), taking advantage of their Winter and of the distances, but it was most often the incoming armies that would plunder for food for themselves, and burn everything left, especially if they needed to retreat (anyway, they would not have cultivate the land).
The historical reality about castles is much grimmer than what many movies and some tales, even inscribed as part of official history, make it.
Especially as the population increased, but even during most of the medieval period (aside maybe the occasional plagues, when the population shrank, and even there, to be seen), most medieval castles did not have the capability of hosting all the peasants spread in the land under the control of the noble or king for a long siege.
Most had a well, only very few a source, and that could take care of water, but the well could be enough only for a limited number of people.
It is true that a number of castles were also supposed to offer some protection to the peasants living close to it, but in general it was really only a subset of all the peasants under the castle's authority, or from raiders that would pass and go, not a prolonged siege without receiving external help for all the peasants living under the authority of the castle's noble (at least, unless the castle had a very small area under its formal control).
Especially peripheral castles like would be Cliftonhold, had relatively limited storage capability, and they did not have stuff like our fridges and freezer to keep food for a long time.
There are known cases of very long (years) sieges, but they were mostly fortresses or fortified cities, not castles, exactly because a years long siege requires either to have ways to sneak in and replenish reserves, or to have long reserves.
It is not by chance that many sieges ended either by starvation of the ones under siege, or by sicknesses that developed due to the concentration of people inside the fortified place much higher than normal for too long (when not directly fostered as a kind of biological/batteriological weapon ante litteram).
The Khan does not look like a good military leader if he relies only on that without a backup plan 
In his case it can be granted attribute to excessive self-assurance/arrogance by the Khan, however, it is far from strange.
In business (and in life, when possible), it is good to have always a plan B, in services likes airlines they should have an entire alphabet
of options, in space business they are supposed to have manuals detailing the procedure for any possible failure/problem, etc..
But miliitary typically have one attack plan.
They can have multiple scenarios covered in terms e.g. when defending, "if attack comes from direction A we do this, if attack comes from direction B we do that", when attacking, "if we attack A we go this way, if we attack B we go this way" (were A, B, etc. can be enemies, specific targets, or specific targets and enemies, though in theory the objective and outcome sought should be the starting point that can clarify whether it makes any sense to even plan any attack in the first place), and they try to e.g. foresee the possibilty a military unit may intervene to support their target enemy (if possible, neutralising them the moment they attack or even before, e.g. to create an attack and/or extraction corridor or avoid they can intervene later and create critical mass or otherwise interfere) but in general they do not create a whole list of "letters" for each case.
In general it is considered that the fog of war is very often too thick, and situations like when the USA gave the Ukrainians the Russian battle plans one month before the Russians attacked (it was revealed a few months after the start of the war) are rare.
They rely more on having e.g. reserves they can mobilise if needed, capability for rapid reaction and decisions, general preparations for anything (e.g. the siege of Alesia, where Caesar prepared an external kind of vallum considering the possibility of help coming for the ones under siege), or such a material advantage that the single operation cannot be at risk (well, boots on the ground change things, but never mind that) than on foreseing all kind of possibilities.
It is part of the reason for the emphasis in more modern times about stuff like satellites, radar, real-time communication and coordination (well, attempts at), to be able, at least in principle, to be aware of changes and coordinate actions and reaction rapidly.
In reality, even in life and business, as a general rule you cannot plan for, and foresee, everything, just trying to analyse before at least some risks, and manage them and others - but that, is a different subject.
The information the Khan has is limited, effectively, he has almost no information, despite what he believes.
It is not suprising he is relying on a "shock and awe" or "overwelming strenght" approach (and yes, I know where I took this phrases from, and it is not a mistake, that is the kind of approach you can take when you know, or believe, that there can be no substantial resistance already at the start and have a huge advantage in terms of quantity).
As far as he knows, Cliftonhold has only peasants armed with old stuff, the mercenaries, and it is half run down already - he does not know all the other things that Luna could do (and depending on the choices, has done) to reinforce its military.
That is, unless
Luna has reject the Baron's offer, in that case, I think the Baron is practically sending information to the Khan, which means, the Khan could get an indication of what to expect..
Yes but unfortunately this game looks like the only one (with LFFG) with fem MC where you build your power base, enjoying relationships with lots of women and destroying misogynistic men. If anyone knows something similar please tell me, I looked around for a looooooooooong time, and it looks like Frozen Synapse work is really unique in that regard.
Well, that is one way to see and play the game, there are a number of others. But your way is as legitimate as any other.
