not really sure where amherst is but you're best bet for backcountry in new england is going to be in the white or green mountains in NH and VT not really sure on specific locations though. I could be wrong, but i'm almost positive there are no decent backcountry locations in MA
MA can get decent amounts of snow occasionally but you're not going to find any back country, unless you head up north more to Vermont / New Hampshire. I hate MA
I line about 20 minutes away from Amherst. If it's a good year we can get a good amount of snow. And aa posted above the best backcountry you will get in MA is mt. Greylock.