Preheat oven to 300°. Line 2 baking sheets with parchment paper.
In a small bowl, whisk powdered sugar, salt, and vanilla with 2 to 2 1/2 tbsp. water to make a thin syrup. Working with one kind of nut at a time, pour in nuts and stir thoroughly to coat every nook and cranny.
With a slotted spoon, lift nuts from syrup, letting excess fall back into bowl. Spread nuts on baking sheets so they are not touching. Repeat with each type of nut. Bake 12 minutes. Cool until crunchy, then flake off excess sugar.