Cotton has its downsides, but then so do synthetics, so it's horses for courses!
When I'm walking with a heavy pack I usually wear a synthetic wicking base layer (with built in mosquito repellency!), with a supplex nylon shirt over the top (Air Land & Sea). The shirt has mesh covered vents in the back, loads of pockets, adjustable cuffs and button secured roll-up sleeves. I run warm, so tend not to wear anything else on top of that while on the move, just adding a fleece when I stop, unless it's raining of course. I've found that this synthetic layering principle massively improves the sweat problem, and vitually eliminates clamminess. My back still gets wet, but after 10 minutes with my fleece on at rest, I'm a lot more comfortable. My cotton layering used to stay wet for hours. As Squidders says though, this isn't that relevant whilst pottering about in the woods.
Also synthetics smell horrible, especially after a few days, so you need to rinse them out when you can. At least they dry quickly.
When I get to camp I like to change into cotton, particularly to sleep in, as it smells less and feels more comfortable on the skin. Wool generally makes me itch and is too warm, but I am getting some Ullfrotte long johns for Christmas, so we'll see if the non-itch claims are justified!