Answer:
No. Possums do not hibernate. They remain active through all seasons. True possums are native to Australia, New Guinea and Sulawesi, and are quite different to the North American opossum.
However, the Mountain Pygmy Possum is a tiny possum which lives in the Alpine regions of Victoria and New South Wales, and it does hibernate, for between three weeks and three months. It is the only Australian marsupial which hibernates.