Cotton is the worst cold-weather material. By its nature, cotton is a highly absorbent fiber that loses all its resiliency and springiness when it gets wet. That lack of wet-weather backbone causes all of the tiny air pockets that really provide your insulation to collapse and disappear. To make matters worse, water conducts heat about 20 times faster than dry air, ten times faster than dry cotton. If your cotton T-shirt or sweatshirt gets wet, you've got the worst of both worlds: no air pockets to provide insulation, and a dense mat of saturated, highly conductive fibers clinging to your skin and conducting heat like crazy. Water evaporates directly off your skin, increasing your frigid misery. To add a final insult, cotton clings tenaciously to the water it absorbs, so it dries on a geologic time scale.
Wool shares cotton's bad habit of sucking up water like a sponge, but it has one redeeming feature that made it the fiber of choice before synthetics: it retains its resiliency when wet. That means it retains its ability to trap tiny air pockets and won't collapse against your skin like cotton. The problem with wool is that it dries just as slowly as cotton. If the sheep from which it came happened to have a particularly dyspeptic disposition, it also makes my skin itch and even break out in a rash. On the plus side, if economy is your main criterion, you can probably pick up military surplus woollies for a song. Just be aware that you may be singing the blues if they get wet the first day, because they'll probably stay wet for the rest of the trip.
Synthetics offer three significant advantages compared to cotton: they retain their resiliency and insulating capacity when wet; they absorb very little water; and they dry fast. In addition, synthetics are generally more abrasion-resistant than natural fibers, so they last longer. Polypropylene was the first synthetic to be widely used in outdoor clothing, but it quickly came under fire for its rather harsh, plastic feel, its penchant for shrinking into doll clothes if thrown into the clothes drier and its tendency to lovingly embrace body odors and refuse to let them go, even under threat of repeated washings in paint thinner. Polyester seems to be the material of choice now for long underwear and for the large and varied assortment of thick, heavily napped fabrics loosely called pile or fleece. Polyester can be knitted into lightweight, wonderfully soft and comfortable styles for long underwear and bulkier forms for sweaters and jackets. It doesn't cling to odors as much as polypropylene and bears up well under normal washing and drying procedures. Nylon, while ubiquitous as the shell fabric in rain gear and insulated parkas because of its great strength and abrasion resistance, is rarely used in insulating clothing.