How cold does the Winter get in these Areas?
Eucalyptus trees live in places where the temps drop below 10C in winter. Look up Mt Kosciuszko. Tasmania can get even colder during their winters. Tonight for example, Hobart at 7:30pm their time, registered 78kph winds, 42 knots and their apparent temp, dropped to -5.5C, recorded temp without the wind would have been 5.8C because of the SSW gale blowing through there. Coldest overnight they have had there is 0.4C
Edit to add
Mount Wellington which is about 8km west of Hobart dropped to -2.7C with wind temp at -26C with the wind gusting at 130kph.
So, one could say in Tasmania is gets damn cold, and that's putting it politely.