I do not know how far is this from Zero CO2 considering cattle production and CH4 emission, cement production, ship and airplane traffic ...
(Natural Gas in Australia isn't that cheap anyway, we export nearly all of ours)
We have gas heating, floor heating , wall heaters and such..
However the weather doesn't get cold enough to kill you here even down south. The houses generally aren't designed for cold weather and we as a nation tend to just put on more clothes and endure somewhat colder houses. I've had people from overseas complain about how cold they get because we don't do much about it.
In say, Germany/China in winter I remember being stunned by how hot people kept their houses and public spaces. We don't heat our spaces in the same way generally.
On the other hand, it gets real hot and we are somewhat optimised towards that way of living.
Average daily winter temps in Hobart (capital of Tasmania) is 8.5C (47.5F). It snows enough for ski resorts in Tasmania [1]
So yes.