The only time I have sailed the Tasman ( Bass Strait to Cook Strait) was in late January.
However..... in the day job I spent about 18 years on Bass Strait ( about 3300 crossings more or less ) plus 3 years before that running across the Bight to the west and also a couple of years on rig boats in the Paddock. Also about 20 years small boat sailing in the area in all seasons.
Winters can give very settled weather
, depends on the year. Gales are usually quite honest... you see them coming and.. well.... they are just gales.
Worst time is typically August/Sept with April not quite so bad...the equinoctial gales.
Late spring/Early summer gives storms... not many but can be bad... short sharp and nasty... from October into very early January.
So nothing intrinsically wrong with a winter crossing ( depends a lot of course on boat and crew).
Problem is picking if it is going to be a hard season or not, dry year ashore...good winter weather
Dunno if I would be wanting to make a landfall on the west coast
of the South Island in winter..... maybe I'm just getting soft.