"AND, having been there near Thanksgiving and camped near a couple of hunters, they told of caching stuff there for a mid-January party, wherein (and here's the point, again) they get in on snowmobiles."
The Wild River Rd. is closed to snowmobile traffic according to WMNF regs. so those hunters were planning on doing their trip illegally and would need to circumvent the gate somehow.
"Add it all up, though (if you have mapping that does that): it's a long haul from Gilead/Hastings all the way back in to the Wildcat River trail. Yes, you could almost certainly do it as a ski (if you're fit), but it seems to me it would be a pretty long snowshoe day."
The shortest route, and the one recommended by Goodman, is via the Bog Brook Trail from the end of the plowed section of Carter Notch Road. Special note: you will need to park further back down the road than the very end. Jackson XC Center shuttles use the end of the road for a turnaround and so parking is not allowed there. There is a parking lot about a 10 or 15 min. walk back.