I was over there in Jan/Feb and had the best weather possible! It's going to be cold for you!
Definitely go up Mount Wellington (one of the best things, photographically, I did) - I swear my fingers nearly fell off from being so cold though and that was in 'Summer', so good luck. Whilst in Hobart, go and see Strickland Avenue Falls and O'Grady's Falls, well worth it.
It's also well worth making the trip out to Huonville (40min out) and dropping in at Willie Smiths. Best cider I have had and a really cool place! If your in Huonville, you can drive out to Snug (can't remember how long that took, maybe an hour) and see Snug Falls too.