Note, though, that skiing drains fatigue regardless of skill (high skill means lesser, but not zero drain), which means hunting during the winter is currently a fair bit harder than during the snow less seasons (an on top of that you need to encumber yourself with heavy clothing...).
As noted, you can't "run" with skis (apart from an exploit), and skiing isn't faster than walking currently.
Skiing is probably the easiest skill to improve, though, so you'll probably be at 100% after the first winter.
I assume you've seen this, but it's easy to forget to re-equip the ski stick after having performed activities, so you actually walk around on skis, gaining no benefit from them (and it doesn't help that the feedback indicating your state doesn't update when you equip them, but only after having moved a tile).