Threadbare argument
I think it's a long way from our atmosphere to your hypothetical blanket, but as you want to draw a parallel between the two, then yes, I think it's safe to say that a threadbare blanket with three or four flecks of down for every 10,000 (empty) threads would not do much to warm your buns or cover your nakedness.
To be precise, the argument was made by Gerlich and Tscheuschner, but let me ask you this: if we have in fact entered a period of cooling, does that by itself falsify the theory of AGW? Indeed, how can we tell for sure if the planet is getting warmer or cooler? If the latter, will wind farms and solar power keep us warm?
S