For serious or slow trips, undergloves and underclothing help keep you warm. If you think that you will get too hot, pack extra clothing in your pack or dress so that you can remove layers of clothing as needed. Good footwear is also needed. A vibram sole with deep lugs is a good choice. A good sole will help you get good footing and help prevent slipping on uneven or slick surfaces.
Shoes can be either low or high top but good ankle support is preferable.
To help keep your feet toasty warm in wet caves, try neoprene wetsuit booties. They are well padded and help keep your feet dry. Another way is to wear wool socks with polypropylene sock liners. A neat fitting pair of gloves should be worn to protect your hands. They will also keep your hands warm and relatively clean.