Heavily grease and flour the donut pans. Set aside.
In a large bowl, whisk oil with apple sauce, apple cider, and sugar. Add eggs, vanilla, cinnamon, baking powder, and baking soda, whisking until homogenous. Slowly add flour, mixing until just incorporated.
Divide mixture into donut pans, filling about ¾ of the way. Bake at 350°F for about 12 to 16 minutes, until slightly golden and set. Cool completely before removing from pans.
Freeze for about 30 minutes before dipping in white chocolate glaze.