In a medium size mixing bowl, combine the sweetened condensed milk, pumpkin puree, spices, pudding mix and a good splash of water (about 1/4 cup). Using an electric mixer, beat everything together until smooth and thickened, about 2 minutes. Set aside.
In a large mixing bowl, whip the heavy cream with an electric mixer until stiff peaks form. Gently fold the whipped cream into the pudding mixture until blended and no streaks of pudding remain.
To assemble, layer the cookies and pudding mixture in a serving dish (or several individual dishes) in whatever fashion you like. Cover the pudding(s) with plastic wrap and refrigerate for at least 2 hours and up to 8 hours (you want the ginger snaps to soften up from sitting in the pudding mixture).
Top with some ground cinnamon or more whipped cream if you like, and serve cold.