Yes we do have canadian geese over here, however we have no snows. We hunt 'em over most of the country however I believe the lower south island has the best hunting for them.
Seasons and limits vary depending on the region (in some regions they are considered noxious). In fact in many regions there is no limit. And the licence to hunt them costs $72 for the season. For rules and regulations go to www.fishandgame.org.nz
. They are also the people to contact regarding access.
If you have any other questions I'd be more than pleased to help