As you know, the premises on the LSAT have to be taken as true. The jump from the premise about keeping your hands warm by keeping your vital organs warm is in the degree of strength – we go from you CAN do this, in that premise (that is, it’s POSSIBLE), to you can ALWAYS do it with an extra layer of clothing, in that second sentence, which I see as the intermediate, or subsidiary, conclusion. That certainty is carried over into the main conclusion – “never.”
But honestly, going back to my earlier post on Strengthen/Weaken questions, I wouldn’t hit this one with that level of analysis, most probably. What’s the conclusion? The first sentence. On a weaken question, I’m looking for the answer that makes the conclusion less likely to be true.
If the conclusion is “you NEVER need gloves or mittens,” then I want an answer that suggests that sometimes I actually might need them, and (C) gives me that – it tells me that under certain conditions (at certain temperatures), that extra layer of clothing isn’t going to keep my hands warm. Since that’s the only alternative to gloves and mittens proposed by the passage, now I’m back to think I probably *do* sometimes needs gloves or mittens (or at least possibly), so there’s a decent chance the conclusion is wrong, i.e. the argument is now weaker.