Cold doesn't harm plant cuttings, as long as they don't freeze. It is high temperatures that quickly convert them to green mush. When I mail cuttings I put the wet cuttings in a dry paper towel, and put that in a ziplock bag. I use priority mail boxes, so I just stuff the bag in the box and add some crumpled paper if necessary to keep them from bouncing around.
I did a test a year or so ago, where I packaged plant cuttings in three boxes, one with wet newspaper, one with a dry towel, and one with no towel at all, just damp plants in the bag. Then I left them in the back of my car, for 3-4 days, with the car in the sun a few times for a half hour or so, the rest of the time in my garage. When I checked the plants afterwards, all were about the same, with one type of plant in bad shape, and the others in good shape. So, a lot depends on the plant being mailed.