In the winter, some people travel on boots. Some are on snowshoes. Some are on cross country skis. Many of each category use poles for balance. Some poles, especially for skiers, have wrist loop straps. Wrist loops can be adjusted, with difficulty, to accommodate bare wrists, thin gloves, or bulky mitts. You don't want to have to change back and forth much.
So, during hours on the trail, I normally wear thin wool gloves or thin polypro gloves, and my pole straps are adjusted for that degree of bulk. When I arrive in camp, I might have to build a snow shelter or something, so I can don the bulky mitts, but I won't be using any poles then.