I'm surprised we're even talking fire starting. I take redundant fire starting (lighter/waterproof matches/firesticks) every time I go in the woods seriously. Doesn't everyone, and especially in winter? It's part of a zip lock that contains compass, knife, some cord, tiny first aid kit (w/ usual assortmet of stuff including duct tape), head lamp and in winter, space blanket and chemical toe warmers. In full winter, I also always have crampons if going up a mountain.
Other than that stuff which goes everywhere, it depends. On one of my couple winter trips up Liberty each year (a mountain I like, two hours from door to trailhead), not much else except redundant (BTW, I'm not an engineer, I just like the word redundant today) socks, gloves and hat. Generally goggles and balaclava too along with the normal winter wear and normal food for winter day hike (I usually carry a thermos with soup too). The generally below 4000 trips in snowy woods (versus icy ledges), I have found you don't need to overkill.
Above treeline, GPS goes in, axe straps on too and at least, pad/sleeping bag and heavier space blanket tarpish thing.
I hike alone a lot in winter and like others mentioned earlier, always stick to the route (but I leave what the likely "out" alternatives are as well). And whether alone or in a group, the key word in winter is conservative.
Conservative miles, turnaround time, goals, reaction to weather, etc.