I'll take a stab at this. I think what you'd get is a gradual of progression that starts out well for your talented minority (I'm assuming the 'special' people are the exception rather than the rule) but then gets progressively worse.
Upon closer inspection, my interpretation diverged somewhat from the stated conditions. Basically I missed the second half of the third paragraph ("special skills can be learned by anyone..."). The assumptions used below are:
People possessing the special skills are a minority group within the planet's population, and stay that way.
Whether or not someone possesses the special skills is an innate attribute; they're either born with the capacity or not.
The capacity to perform the special skills is hereditary, passed on through a recessive allele; if both parents are skilled, then their offspring will be too, and if only one parent is skilled then there's either a 0% or a 50% chance that each child will inherit the trait (depending upon whether or not their partner has a copy of the recessive allele at all).
The ability of 'normal' people to learn the special skills is limited, at best. Perhaps they can pick up a few basics, but without the innate talent their abilities never amount to much more than simple parlor tricks.
So in other words, I assume that the special group of people are special not just because they know things, but because they possess some innate attribute that allows them to do things that other people just can't. The scenarios below flow from this assumption.
The Early Days
Chaos reigns amongst the general population. The conditions on the planet have taken a drastic turn for the worse, many have died, and so on. Whatever social order may have previously existed has been shattered, and you're left with pretty much a blank slate. Survival is the only game that anyone is playing.
During this time one might expect members of your specially skilled caste to be viewed similarly to wizards in your stereotypical fantasy context. As in, greeted with instantaneous awe, respect, and blind devotion. Moreover, you'd likely have permanent settlements spring up around these people (because where else is settlement possible?), and it's likely that at least some of them (if not most) might nominally be viewed as the "leader" of their local village.
Probably there'd be no over-arching social structure at this point, with each village essentially having its own set of rules/customs/laws. There may not be any significant interaction between settlements, because each one survives by virtue of its local "wizard", so what point is there in engaging with others?
The problem is, once the basic survival needs of everyone in a settlement are being met, their thoughts can turn to other things. And people don't generally like being beholden to others for their survival, especially if they have no direct influence over those others.
And unfortunately, unlike wizards in a fantasy setting, your special individuals don't have godlike combat abilities, or superhuman wisdom/insight, or anything else that would reliably protect them from the self-serving machinations of others.
Eventually somebody is going to work out a way to put a yoke around their neck, and take control of the situation. It's not hard to imagine ways in which they might do so:
Create an 'if you let me die, then you'll die (and probably slowly/painfully/horribly, too)' kind of situation. For instance, kidnap the special person, lock them in a room where nobody else can find them, and suddenly you're their only source of food and water so they can't let you die and you're in a good position to exert leverage over them in terms of getting them to do/not do other things.
Create a 'do what I say, or your friends/family/dog/cat all die' situation. Probably a riskier gambit than #1, but someone is bound to try it.
If a member of the opposite sex (or same sex, in the instance of gay special people), use seduction.
Use manipulation and/or take advantage of their core principles. For instance, contrive an incident that allows you to "save" the special person's life, and have them swear a life-debt to you in return.
Anyways, as time goes by I'd expect that nasty, brutish, 'feudal warlord' types would start finding ways to dominate and control at least some of the special people. Depending upon how easy/effective it is to do so, any independent special people might find themselves subject to organized hunting efforts and face gradual subjugation as a result (and who knows, maybe subjugating one is a way to gain significant status in the emerging social structure, as it means you're now self-sufficient and have the means to support others of your choosing).
Since it takes a brutal, scheming, power-hungry sort of person to subjugate another in this way, the rest is fairly predictable. The special individuals are no longer the local leaders, and their replacements will work tirelessly to build up their influence and power for its own sake. Shifting conflicts and alliances between settlements/their leaders seem likely, Game of Thrones style, as each local despot jockeys for the top spot.
And as long as the 'normals' have control over enough special people to ensure their survival, any others are essentially expendable and too dangerous to allow to roam free (for fear that they'll agitate/liberate others). Without significant foresight (to the extent that some large segment of the special individuals see what's happening well in advance, and agree to work together to stop it) and plenty of luck (they're heavily outnumbered and have no particular skill when it comes to combat or strategy), the vast majority of them will be either subjugated or killed. Dark days, indeed.
The End Game
Long term, I think a stable equilibrium may be reached in which the output from the special caste of individuals is essentially commoditized and tucked away somewhere out of sight where nobody really sees (or cares about) what's going on.
You could, for instance, have a 'corporatocracy' kind of situation where a single entity has control over the entire caste and coordinates their output for the rest of mankind (at prices that essentially make slaves out of everybody, of course). Forced breeding and/or cloning programs may be employed to keep up numbers, along with indoctrination/brainwashing of new children to make them more easily controllable. The controlling entity just needs to keep them comfortable enough that they're more willing to play along than they are to die in protest (or to be less dramatic, to lose out on some of their comforts in protest). Nobody else can see what's going on under the covers there, so nobody else cares (even if they might due to prevailing social mores).
Or, as already has been mentioned, kind of like farmers in the real world (or Navigators in Dune, floating around in their vats of spice, happy to just sit there, get high on spice, and ferry folk around for the Spacing Guild). But potentially much more brutal depending upon what sort of culture develops on your much harsher and less habitable planet.
Your special individuals have something that everybody else needs, but lack both the brute force and the intellect to prevent others from taking it "by hook or by crook". Other people maximize their benefit not by playing nicely, but by establishing themselves in a position of control/dominance over the special ones. The economics of the situation are heavily against the special people, and unless your society is a very altruistic one things probably won't end up well for them.
A benign subjugation is the best plausible outcome.