The Hakuba shuttle stops right at the Powder Temple's front door. Using this shuttle you can pretty much get to anywhere in the Hakuba Valley, including the mountains.
The closest mountains to the Powder Temple are Hakuba 47, Hakuba Goyru and Happo One (pronounced o-ne). A little further a field is Iwatake, Cortina and Tsugaike Kogen. There are also a couple of other snow fields around if you would like to go exploring.
Although you are able to get around quite easily by shuttle, hiring a car is an attractive option if you would like a little more freedom.
Windy Car Rental is a local rental agency that has a range of small cars all the way through to 10 seater vans, all of which are 4 wheel drive and come standard with winter tyres. They can be booked directly through their website - http://www.windy-kobeya.com/car-rental/