Hi,
How about South Island New Zealand. Queenstown / Wanaka region. Ski season starts early June in this area. It will be early season for the ski resorts slopes, so questionable snow levels at lower altitude in early June, but higher altitude mountains surrounding these 2 towns will have snow. If you are not looking to necessarily shoot on a ski field then there will be lots of mountain options with snow at higher altitudes.
Good infrastructure for filming in these areas, with many crew based in Queenstown.
We have a large database of Mountain / Snow images of this area, and scouts on the ground in Queenstown
Cheers
Richard
http://www.hotspotslocations.co.nz