Distance: 8.4 km (7.0 DOC hours) - Unmarked route, clear - Moderate terrain
Altitude: 921m to 1518m. Gain: 760m. Loss: 1190m . Gradient: 13 deg (Moderate-hard)
Skills: Alpine weather (2/7) Winter - Snow/ice underfoot (2/7)

Unmarked route, clear (7/9)
Unmarked route, follows obvious geography (river, spur, trail, etc)

minor (5/5)
A viable route, not widely used

Moderate-hard (difficulty: 4/5)
Continuous moderate climbs

Moderate (difficulty: 3/5)
Low scrub in open or bush / river rocks

Alpine weather (difficulty: 2/7)
Tramp on open tops, exposed to alpine weather

None (difficulty: 1/6)
No unbridged river crossings

Snow/ice underfoot (difficulty: 2/7)
Snow/ice likely on track

I did it on January 1st. Winter would be doable on a nice day, but running out of sunlight would be an issue as would the weather. It's open, exposed travel to start with and depending on direction, another 45 minutes at least to Kime hut or several hours to a hut from Cone.

From Hector, head off down the clear open ridge heading ENE. Fill up your water bottles at one of the huts before Hector, or small tarns on this ridge about 75m off Hector - there is now water at the new Wincombe Biv.
The route is fairly obvious over 1398, Winchcombe as it is in the open, then it drops into the bush. Neill is out in the open again and would be a nice campsite if there was water. While the ridge looks fairly level on a map, there are a lot of short steep climbs and drops. It can be hard work.
Through the bush, there are old markings, many of which are covered in thick moss on the trees. The track is fairly easy to follow, but we found it hard to follow coming up out of Neill Saddle to 1118. It's easy from there to Cone. There is good camping on Cone next to the tarn - there are some nice spots tucked out of the way - it's worth looking around. The water is an interesting colour - you will probably want to boil it.

Note: Described in the reverse direction to your journey

From Cone tarn, head SW to the junction, then W, dropping down to 1118, then head in a NW direction dropping down to Neill Saddle. The track is hard to follow on this stretch and the ridge a bit broad. From Neill Saddle, the track is easier to find, just head up (and up and down) along the ridge to Hector. Take plenty of water - there is unlikely to be any until some small tarns just to the ENE of Hector on the Neill Winchcombe ridge. Note there should be water at the new Winchcombe Biv. You may find water at the old Winchcombe biv site occasionally. If there was water, camping on Neill would be nice. While the ridge looks fairly level on a map, there are a lot of short steep climbs and drops. It can be hard work.
There is good camping on Cone however the water is an interesting colour - you will probably want to boil it.. there are some nice spots tucked out of the way - it's worth looking around.