I don't think that wet wool truly keeps you warm. It does provide insulation that some other fabrics do not and it does not rob you of your warmth like some fabrics do. It also dries fast and wicks well, so that helps.

But any wet fabric is not going to be as warm as a dry one. I would say that a wet wool jersey is going to be warmer than a wet cotton one. Or, at least, that's been my experience. Of course, wet is still wet and that is rarely comfy for extended periods no matter what the fabrication.