Aborted a couple of attempts at Ossa in winter because of deep snow and ice. Attempted Pelion East with care instead - again, ice was the main issue. We got to the last scrambly bit (very carefully, in places), but there was about 3 cm thick smooth, rounded ice on the rock we had to get ourselves up onto. 2 of the 4 of us were very keen ready-to-climb-anything-possible types, but without any specific gear for ice. They gave up after the other 2 of us had sat enjoying the sunshine for a good 20 minutes. It's not worth taking any risks with ice. People fall off things and do bad damage or die (as someone did not too long ago off Cradle).
If it's icy, Mt Oakleigh is an excellent alternative. (Well worth doing anyway!) I haven't done it since the boardwalk was put across the boggy plain, but I suspect you no longer have to do a dance through the upper branches of the shrubbery to get across the creek in the middle of the plain when the water level is up. It's one of my favourite mountains - just gorgeous looking down on the spires and little rock gardens. Great views, and it gives you a great perspective on the various levels of plains and valleys of that part of the OLT. And I don't remember any rock scrambling to speak of.
I agree with others who have suggested that there's a big jump from the experience you mention to doing the OLT in winter. Sure, conditions could be lovely (you just have to plan according to the short daylight hours), but I reckon the chances of things going pear-shaped in winter, when you haven't been in those conditions, are much greater than in summer. Much smaller margins for error. Prepare plans b and c (elsewhere in Tassie) in case the forecast is lousy. There's a wealth of magnificent walks here.
More choices if you have transport of course.