12 potentiometers with multiplexer
The input circuitry on an Arduino will work "best" when you use pots that are 10K or less.  This has mainly to do with how long it takes to charge up the internal circuitry to get a stable sample.  Since you don't really want to go into the guts of the Arduino libraries to wait extra time between initiating the sample and reading it, you're best off following the 10K recommendation, unless your application is not a precision application (and you haven't told us).  When you're multiplexing 12 channels though, things generally run pretty fast.

If you're really trying to go low current, you can keep using the 100K's, and just put a voltage follower on the output of the multiplexer.  

Yes, 100K pots will cause more noise than 10K pots.  How important this is to you depends on what you're actually trying to do, how precise your measurements need to be, etc., and we have none of this information.  I suspect that the noise difference will not be an issue for you.