well you won't see snowfall here like at Tahoe.... when i was there they got more in one day than we had all year round! (or was that copper mntn... either way!)
but you have the hypothermia risk here due to cool temps, wet + wind in Tas. - generally not such a frozen terrain..
Theres a nice loop track in Katoomba to Mt solitary and back via wentworth falls (from memory) in the blue mountains, NSW
Tassie has lots of walks and the whole state would be maybe about a 4 - 6 hour drive end to end so less travel time i guess...
The Overland track is fairly well populated that time of year so expect company.
The south coast track is really nice but more mud, probably not snow...
there are some good guide books around.... John Chapman is a reputable author for eg and there are some really good guide books around for the overland track especially..
Maps in Tassie can be bought through "Tasmap" and are available online for purchase...
Mt Anne circut to Lake Judd (or lake "Mud" unless this track has been fixed up since i was last there) is nice depending on weather ( esp. windy)
I think Western Aus is better suited for winter months - too hot n dry in summer - and water is heavy
Tassie is great for natural water supply but a LOT steeper than WA... I just moved back to Tassie so i am biased! more than a lifetime of walking available there.
theres also a section in this forum for finding walking companions etc so if you wanted to find others or maybe local walkers that might be worth a browse or a post there too....
scrub here can be thick and sharp and make ya wanna crawl up in a ball sucking on chocolate n moonshine on a reality escape so i would try to stay on tracks at first.... Bring a stove too as many areas here don't allow fires.... theres a track report section in the WIKI section here as well as gear suggestions etc....
With your planning etc, youre gunna have one GREAT TIME i think

From the sound of it fitness or altitude won't be such an issue for ya

when your here give us a holler too - i might need to escape the missus n kids for a day or two by then