Hi Ted,
Drive to skifields are an option, but you can check out the latest conditions here on the webcams.
http://www.snow.co.nz/mthutt/snowreport/
This is the closest to Christchurch and as you can see we are still someway off getting decent cover. The Queenstown fields are still some way off being ready as well and look worse than this. These days the best conditions are usually mid July till end of August for skifields if you want decent snow cover.
At the moment the weather still feels quite mild and I don’t see too much changing between now and early June unless we get a radical change with the weather pattern.
So your best bet for New Zealand is to be looking at the highest mountains for a location.
Hope this helps.
Kind Regards
Rob