Line 2 baking sheets with parchment paper. Spread the nuts on one sheet and toast in a 325°F (165°C) oven for 8–10 minutes until fragrant. Cool completely, then chop very finely (or pulse in a food processor in short bursts).
In a large bowl, rub the orange zest into the 2/3 cup powdered sugar with your fingertips until the sugar is aromatic and lightly tinted. Add the softened butter and beat with a hand mixer on medium speed until creamy and smooth, 1–2 minutes. Beat in the almond and vanilla extracts for 15 seconds.
Whisk the flour and salt together in a separate bowl. Add half to the butter mixture and mix on low just until mostly combined. Add the remaining flour and the cooled, finely chopped nuts; mix on low only until no dry streaks remain. The dough will be soft but should hold together when pressed.
Use a level tablespoon scoop to portion the dough onto a prepared baking sheet. Roll each portion quickly between your palms to form smooth 1-inch balls and space them about 1½ inches apart.
Chill the shaped cookies on the sheet until firm, 25–30 minutes. During the last 10 minutes of chilling, increase the oven temperature to 350°F (175°C).
Bake one sheet at a time on the center rack for 14–16 minutes, rotating the pan halfway through. The cookies should look set and dry on top with only the bottoms showing a pale golden ring.
Set the pan on a rack and let the cookies cool just until they can be handled, about 5 minutes. Place the 1½ cups powdered sugar for coating in a shallow bowl and gently roll each warm cookie to coat. Transfer to a rack to finish cooling.
When completely cool, roll the cookies a second time in fresh powdered sugar for a thick, snowy finish.