Wool absorbs moisture, just like cotton. The only difference between it and cotton is that wool still has some insulation value when wet, whereas cotton does not.
IMO, cotton does not have ANY use in my hunting clothing (or skiing or ice climbing or whatever else in cold weather) whatsoever. It is comfortable when dry....and that's about it. I don't want anything that HOLDS moisture in my gear. Period. Why hold when you can wick instead?
While the idea seems logical, imagine wrapping a wet towel around your wool sock. Some moisture is going to transfer back into the sock, or, at the very least, just prevent the sock from shedding some of the moisture off of it. Is that what you want?
Wicking works as follows: body heat drives moisture away from the heat source through fibers that DO NOT absorb moisture (synthetic). Why would you inhibit that process intentionally? You don't need to put a cotton sock on to help pull the moisture out, unless your first layer doesn't wick (100% merino doesn't wick very well). Your boot is going to stop some moisture from wicking anyway. I'd leave it up to the boot. Get some merino/synthetic blend socks and go from there.