Yes, all the passes will still have a lot of snow on them and you will need an ice axe and crampons (and know how to use them) to go over them.
Greenstone-Caples would be a very good trip to do.
You could also walk up the Wilkin valley and spent 3 days exploring in that area (although you should seek advice from DoC about the avalanche risk)
cheers
Richie