Andrew, the fact that you need ask these questions suggest you are out of your depth on this one. Besides the whole route being covered in snow, which can be knee deep slush or ice-rink hard, weather conditions this time of year are potentially deadly and unpredictable, you need specialised equipment (sleeping bags, clothing etc), and significant skills and knowledge, to travel this area safely and comfortably. Snowfalls can occur any time of year, and usually do up until Christmas, as can rain storms just above freezing temperatures, which is potentially worse. In the area you are thinking of doing, there are only two shelters, both notoriously difficult to find in bad weather. There are many other potential problems. Several years ago a person was lost in this area, despite being trained Canadian military - presumably fairly skilled in winter survival. His remains were never found.
Please do your research, ski.com.au, weatherzone, Kosciusko National Park website and
http://www.bushwalkingaustralia.org provide useful info which you need to study. No one in the bushwalking fraternity wishes to hear about disasters and tragedies in what should be just beautiful places, so please take more care than you think necessary. I suggest you look to do this hike between Christmas and Easter, after doing your homework.
If you do end up completing this hike, let the forum know, posting your most valuable lessons.
All the best,
Skibug.