It would be 5 1/2 to 6 hours each way... Go to Canberra down the freeway, then head to Cooma, then to Jindabyne and you're practically there.
Good thing about having a Stagea is that all wheel drive cars dont HAVE to have snow chains onboard
Entry into the national park is about $18/day for a car. You can buy these passes at the Jindabyne tourist information centre or at the entry into the park. There's free parking at the slopes and a good mini mall that has places to buy food, hire equipment, etc... but if you just want to dick around in the snow put on lots of warm layers, a good windbraker and waterproof gloves and shoes Oh yeah... take a change of socks and an extra pair of shoes. They WILL get wet and cold and you will be miserable on the way home if you dont.