Yes you could enter that way, but that would be one long boring unrelenting uphill slog. I'd do it on skis - with the anticipation of the downhill run at least!
There is another way in from the east, but it is a bit of work.
You could drive in to Laneville, and if it's plowed as far as the bridge over Red Creek, shovel out a place to park as close to the bridge as possible.
At the west end of the bridge (laneville side), there is a trail that goes strait uphill - part of the old abandoned high water route along red creek.
If you take that trail, it goes up and ends at an old railroad grade. Turn right and head upstream along the grade.
The grade runs parallel to red creek for a ways, then ends in a bunch of jumbled boulders. You can do one of two things:
If it's not icy, scramble down the boulders and you will end up at Little Stonecoal Run. I wouldn't recommend this if it's snowy/icy as it's pretty steep in places.
Or, as you are approaching the boulder field, the area between the old rr grade and Red creek opens up enough that you can see red creek off to your right. Scramble down off the rr grade here toward Red Creek. There is a small stream/wash right at the base of the RR grade that you will need to cross.
Walk toward Red Creek, and about half way between the Creek & the RR grade, you will see a fairly obvious way upstream, winding through a meadow & the trees eventually leading you to Little Stonecoal Run. Not really a trail anymore, but pretty easy to follow.
In either case, you will need to cross Little Stonecoal Run somewhere, (It's a fairly deep and narrow cut at this point)
Once across, you will quickly intersect Little STonecoal Trail and you can head uphill to Dunkenbarger, & on up to Big Stonecoal etc.
This avoids having to wade across Red Creek in winter conditions, but you will still likely have to wade across Dunkenbarger run when you get there.
Just one note about being up in the Sods in the winter.
have you ever really looked at the trees at Bear Rocks? They aren't flagged for nothing! When it's windy, it can be brutal, so go prepared for real winter conditions, and please don't underestimate how much work it is to get around in deep snow drifts. It's work even with skis, but man is it ever spectacular! (The boulder fields on Dunkenbarger would be particularly treacherous in icy conditions, and require cleats to navigate safely)
As another thought, you might try contacting the ranger station in Petersburg and talk to them about other possibilities, the Sods is part of their jurisdiction.
And at the risk of getting flamed and banned forever from the UL website, you could also snowmobile up the road to the top and hike from there.
nah........ I won't even THINK of suggesting that :-)