In a large bowl, stir together the pineapple and pistachio pudding mixes until combined.
Fold in marshmallows and pistachios. Set aside.
Beat the cold heavy cream with the powdered sugar using an electric hand mixer or a stand mixer with the whisk attachment. Beat on high speed until medium peaks form and it holds its shape. Use a rubber spatula to transfer the mixture to a separate bowl.
Add the softened cream cheese to the mixing bowl and beat until soft and fluffy.
Use the spatula to scrape it away from the sides of the bowl. Add about 2/3 of the sweetened whipped cream to the cream cheese (the remaining whipped cream will be reserved as topping when serving). Whip the mixture together until light and fluffy.
Fold the cream mixture into the pistachio mixture. Cover and refrigerate for at least 3 hours.
Serve individual portions topped with the reserved whipped cream and chopped pistachios.
Notes
Watergate Salad can be made in advance and stored in an airtight container for 2-3 days. Just remember to cover it with plastic wrap and stir well before serving.