Have you tried using a space blanket? I carry one around all the time. They usually have a silver reflective side and a red side. They fold up to extremely small dimensions for their size (mine folds to barely larger than a pack of Kleenex). Not only can they be used as a ground cloth, but also as a reflector (silver side) and even as an emergency weather cover. Also, they are relatively inexpensive, so no need to worry about wear and tear.
That's a good idea. I used to carry one in a car as part of the "stuck in the snow" kit. I don't know what happend to it though. The last cold winter in the UK was about 20 years ago, looks like it might be one this year. I guess a good camping shop is the place to look.