While hiking in the winter, you should really consider bringing an insulated pad or sleeping pad along with you, even if you are just out for a day hike.
Why? Because it will keep you warmer!
If you stop to belay, cook something, or just take a snack break and are sitting or crouching over the cold ground, your body will actually take on some of the heat (it's a science principle thing) and get colder!
So, fix that!
By adding an insulated pad under you, you can keep the heat of your body from heading to the ground (when that starts to happen, nature tries to put you and the ground at equilibrium and thus you get colder). Not only that, but it also keeps the cold from coming up, and it can be quite comfortable.
What about while I sleep?
Sleeping pads are of course an important part of your sleeping gear (if only for comfort) but they can also provide the first layer of insulation that you need from the cold, cold ground and air. There are some inflatable ones that get up to 3 inches thick (which will help with insulation) and are made of either foil or other material that prevents heat sharing. Down filled is one of the best for insulation! Open or closed cell foam is nice, too, but doesn't compress as well.
And if I'm just sitting?
You don't have to bring one as thick or as full of down if you don't want to, but you still want to bring something with either a foil layer or a layer that is rated to keep out the right temperatures!