Here in Boston, the weather can make walking in the woods challenging. I have a range of clothes and footgear that lets me walk under any conditions. Gore-tex shell and rainpants for rain or wet snow. Various fleece tops and a heavy wool sweater from my mother-in-law cover temperatures down to 0 degrees F.
For heavy snow, I have the snowshoes, and for any combination of water and mud, my Limmer mid-weights.
The most challenging woods walking conditions are when a snowfall is followed by rain followed by a hard freeze. Every surface becomes glazed with ice, and it's difficult to stand up, let alone walk. For those days, and there are many in a typical winter, I now have a set of 10-point crampons. With these on, walking on snow or ice is just like walking on a dry surface. No slipping, sliding, slipping, or falling.
But the best part of an all-weather woods walk is coming home to a warm house full of warm, wonderful people.