I agree with most of the comments above. There is some info in the sticky in this forum I am also currently collating some more info in conjunction with the Do in Queenstown in November - sorry but this is at home and I'm currently travelling.

I think number_6 exaggerates a little. In any given year there might be half a dozen or so days when weather closes roads on the west coast or the main alpine passes. The Milford Road has more closures, but more likely in spring than winter (due to avalanche hazard).

If planning to visit Milford I'd allow 3 days in Queenstown minimum. If flying one or both ways, you'll need this many days to have reasonable shot of clear enough skies. If driving then this means you don't feel pressured to try driving on a day when a 1/2 to 1+ foot of rain falls.