There is an amazingly cute, very old, Kosciusko hut near Mt Selwyn, called 4 Mile Hut. This will be a day trip to the hut, heading out early Sunday morning, stopping for lunch at the hut and then heading back to Canberra in the evening. It's 10 km round trip.
People can snow shoe or ski (I'd recommend telemark or XC. AT gear seems a bit too extreme for this sort of terrain, but if you want to get practice using it, you can. You'll need to have had Seb's sign off before hiring out the AT gear).
Hopefully the trip will be entirely covered in snow, but there is the chance that you'll need to carry your snow shoes / ski gear for parts of it.
Please state your level of experience in the trip sign-up.