Yes, in season. Katherine Cole is one of just six Amherst conservation areas that allow hunting, though the town flags its hunting page as possibly outdated, so check current state season dates before heading out.
What rules should I know at Katherine Cole Conservation Area?
Hunting IS permitted here in season, one of only six Amherst conservation areas where it's allowed; the town notes its hunting-policy page may be outdated and directs hunters to confirm current state season dates.