Lake Mountain is about 2 1/2 hours from Melbourne and is a national park set aside for cross country skiers in the winter and biking or walking in the summer. You will not find ski lifts or resorts here, in fact, they close the park in the evenings, but accommodation can be found down the mountain in Marysville, a picturesque town that was badly damaged in the 2009 fires (or you could stay in Healesville which is only 35 kms away).
There is a building for hire of clothes and equipment, payment of trail fees and park entrance ($40) and a canteen for snacks and hot food. They even have a single toboggan run for families to play in the snow. But outside of this it is quiet and lovely.
As always, it is best to come prepared, since the weather can change quickly for the better or the worst.
http://lakemountainresort.com.au/maps/ski-trail-map
Lake Mountain Ski Guide trail map 2012
Always Restless Feet 