Try a pair of Mechanic latex gloves inside of your work gloves, keeps the fingers warm and the water (melted ice from wood) from coming trough. When it gets below 5 degrees I put plastic bags over my socks as well. You can get the latex gloves at NAPA or ask your favorite take out restaurant to give you a couple of pair.
problem for me is age and damage functions. I am about 1/4 step behind Evil Kanevil in broken and damaged internal components. When I get up in the morning it sounds like someone stomping on bubble wrap for awhile until things kinda slide into to some semblance of the human form. Course even at that point there are some that would disagree about the human form.
