Remove the filling from the vanilla cream cookies.
Place the cookies on a sheet tray lined with wax paper.
Place small ¾-ounce scoops of Ben & Jerry’s Caramel Chew Chew ice cream on half of the cookies.
Position two cookies with scoops of ice cream on top of them next to one another. Place a skewer on top of the ice cream, connecting the two cookies.
Top the ice cream with two more cookies to create two ice cream sandwiches connected by a skewer. Freeze for at least 30 minutes.
Place the chopped white chocolate in a tall microwavable glass and melt in the microwave at 50% power in 30 second increments, stirring in between until melted. Dip the frozen snowmen into the melted chocolate, let the excess chocolate drip off, and then place snowmen on a wax paper-lined sheet tray. Freeze for at least 30 minutes.
Decorate the snowmen with royal icing as desired.