G'day Rod, travelled North on the Barry Way late 2014. Other threads/mentions on here somewhere.
We towed the KK behind Hilux for that trip. For you, downhill windy narrowish until along the Snowy, then windy narrowish uphill to Black Mountain.
We had no problems, take your time, keep to your side of the road and look well ahead across the corners where you can.
A heap of camping spots along the Snowy and to avoid the rat race a bit we camped off to the west on the Pinch River, maybe 5-10mins off the Barry Way, excellent track in there.
Have a look at the old Suggan Buggan slab timber school, the way it used to be done.
The rest of the trip either side of the down/up portions is fine.