If you're planning a long distance walk, then nylon gives you the best shelter for the least weight.

Otherwise, woven poly is the way to go IMO. Cotton is too darn heavy and too darn expensive.

Avoid the cheapo blue tarps (or equivalent lightweights). They're junk. Go for the midweight tarps with UV inhibitors. I have used the translucent ones and the silver ones with great success. No need to send away for these: a decent hardware store should carry what you need.

The toughest poly tarps I've every used are the industrial covers made by Integrated Plastics (IP). I've had a dark green one out in the sun for three years now and it's still intact.

Don't worry about cold weather. I've used woven poly for 20 years and have never had one fail due to the cold. It's the sun that eventually breaks them down.