Tiffany/purpleinopp,
I have a Rex Begonia Vine (Cissus discolor) too and easily water-rooted a couple of cuttings. However, it's really easy to overwinter the plant too. When the plant starts looking sad and discolored due to the cool temps, then bring it inside to a cool, dark spot and keep it on the drier side. It will go dormant and drop its leaves. I put mine in the cool (not cold) basement and only give it a small amount of water if the rubbery-looking stems start looking dry (very rarely.) In spring, you can put it in a warmer spot and start watering and it will come out of dormancy and start growing again. Very easy!
I had to do last minute Coleus rescue yesterday due to the freezing temps predicted. I brought a couple of potted ones inside and have a plastic salad mix container full of cuttings to deal with now. It looks like we barely escaped damage as the Coleus outside still looked okay today.
