In a medium bowl, using a handheld electric mixer set on low, beat together pudding mix and confectioners' sugar, with milk and vanilla, until smooth.
Let the mixture stand for 3 minutes so the pudding can begin to thicken.
Using a large rubber spatula, gently fold in the Cool whip until no streaks remain.
Refrigerate 1 hour before using the frosting.
Notes
Flavors: This frosting works well with other flavors of pudding mix, too.
Refrigerate: After making the frosting, I like to refrigerate it for about 1 hour so it will firm up a bit before using it.
Piping: The cool whip makes the frosting softer than a traditional buttercream, so it doesn't hold piping shapes as well. That said, yes you can pipe it. It's important that you refrigerate before piping it so it has a chance to firm up so it will hold the piping shape. Once piped, I keep my cupcakes in the fridge so the frosting will maintain its shape.
Color: If you're looking for pure white frosting, this isn't your best choice. It has a slight yellow cast from the vanilla pudding.
Mixing: Over mixing can break down the ingredient so just mix until combined.